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Relevant bibliographies by topics / Complex Differential Geometry

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Academic literature on the topic 'Complex Differential Geometry'

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Published: 6 September 2023

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Journal articles on the topic "Complex Differential Geometry"

1

Beggs, Edwin, and S. Paul Smith. "Non-commutative complex differential geometry." Journal of Geometry and Physics 72 (October 2013): 7–33. http://dx.doi.org/10.1016/j.geomphys.2013.03.018.

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Wang, Shuguang. "Twisted complex geometry." Journal of the Australian Mathematical Society 80, no. 2 (April 2006): 273–96. http://dx.doi.org/10.1017/s1446788700013112.

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AbstractWe introduce complex differential geometry twisted by a real line bundle. This provides a new approach to understand the various real objects that are associated with an anti-holomorphic involution. We also generalize a result of Greenleaf about real analytic sheaves from dimension 2 to higher dimensions.

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Donaldson, S. "DIFFERENTIAL GEOMETRY OF COMPLEX VECTOR BUNDLES." Bulletin of the London Mathematical Society 21, no. 1 (January 1989): 104–6. http://dx.doi.org/10.1112/blms/21.1.104.

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Donaldson, S. K. "Some Numerical Results in Complex Differential Geometry." Pure and Applied Mathematics Quarterly 5, no. 2 (2009): 571–618. http://dx.doi.org/10.4310/pamq.2009.v5.n2.a2.

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McKay, B. "Complex nonlinear ordinary differential equations and geometry." Journal of Physics: Conference Series 55 (December 1, 2006): 165–70. http://dx.doi.org/10.1088/1742-6596/55/1/016.

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Anco, Stephen, John Bland, and Michael Eastwood. "Some Penrose transforms in complex differential geometry." Science in China Series A: Mathematics 49, no. 11 (November 2006): 1599–610. http://dx.doi.org/10.1007/s11425-006-2066-5.

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Okonek, Christian. "Book Review: Differential geometry of complex vector bundles." Bulletin of the American Mathematical Society 19, no. 2 (October 1, 1988): 528–31. http://dx.doi.org/10.1090/s0273-0979-1988-15731-x.

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Muñoz Velázquez, Vicente. "The Hodge conjecture: The complications of understanding the shape of geometric spaces." Mètode Revista de difusió de la investigació, no. 8 (June 5, 2018): 51. http://dx.doi.org/10.7203/metode.0.8253.

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The Hodge conjecture is one of the seven millennium problems, and is framed within differential geometry and algebraic geometry. It was proposed by William Hodge in 1950 and is currently a stimulus for the development of several theories based on geometry, analysis, and mathematical physics. It proposes a natural condition for the existence of complex submanifolds within a complex manifold. Manifolds are the spaces in which geometric objects can be considered. In complex manifolds, the structure of the space is based on complex numbers, instead of the most intuitive structure of geometry, based on real numbers.

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Everitt, W. N., and L. Markus. "Complex symplectic geometry with applications to ordinary differential operators." Transactions of the American Mathematical Society 351, no. 12 (July 20, 1999): 4905–45. http://dx.doi.org/10.1090/s0002-9947-99-02418-6.

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Aleksandrov, A. G. "Residues of Logarithmic Differential Forms in Complex Analysis and Geometry." Analysis in Theory and Applications 30, no. 1 (June 2014): 34–50. http://dx.doi.org/10.4208/ata.2014.v30.n1.3.

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Dissertations / Theses on the topic "Complex Differential Geometry"

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Lam, Tsz-fung. "Nesting of 2D parts with complex geometry and material heterogeneity." Click to view the E-thesis via HKUTO, 2007. http://sunzi.lib.hku.hk/HKUTO/record/B39557005.

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Lam, Tsz-fung, and 林子峰. "Nesting of 2D parts with complex geometry and material heterogeneity." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2007. http://hub.hku.hk/bib/B39557005.

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Brown, James Ryan. "Complex and almost-complex structures on six dimensional manifolds." Diss., Columbia, Mo. : University of Missouri-Columbia, 2006. http://hdl.handle.net/10355/4466.

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Thesis (Ph.D.)--University of Missouri-Columbia, 2006.
The entire dissertation/thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file (which also appears in the research.pdf); a non-technical general description, or public abstract, appears in the public.pdf file. Title from title screen of research.pdf file viewed on (February 26, 2007) Vita. Includes bibliographical references.

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Kirchhoff-Lukat, Charlotte Sophie. "Aspects of generalized geometry : branes with boundary, blow-ups, brackets and bundles." Thesis, University of Cambridge, 2018. https://www.repository.cam.ac.uk/handle/1810/283007.

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This thesis explores aspects of generalized geometry, a geometric framework introduced by Hitchin and Gualtieri in the early 2000s. In the first part, we introduce a new class of submanifolds in stable generalized complex manifolds, so-called Lagrangian branes with boundary. We establish a correspondence between stable generalized complex geometry and log symplectic geometry, which allows us to prove results on local neighbourhoods and small deformations of this new type of submanifold. We further investigate Lefschetz thimbles in stable generalized complex Lefschetz fibrations and show that Lagrangian branes with boundary arise in this context. Stable generalized complex geometry provides the simplest examples of generalized complex manifolds which are neither complex nor symplectic, but it is sufficiently similar to symplectic geometry for a multitude of symplectic results to generalize. Our results on Lefschetz thimbles in stable generalized complex geometry indicate that Lagrangian branes with boundary are part of a potential generalisation of the Wrapped Fukaya category to stable generalized complex manifolds. The work presented in this thesis should be seen as a first step towards the extension of Floer theory techniques to stable generalized complex geometry, which we hope to develop in future work. The second part of this thesis studies Dorfman brackets, a generalisation of the Courant- Dorfman bracket, within the framework of double vector bundles. We prove that every Dorfman bracket can be viewed as a restriction of the Courant-Dorfman bracket on the standard VB-Courant algebroid, which is in this sense universal. Dorfman brackets have previously not been considered in this context, but the results presented here are reminiscent of similar results on Lie and Dull algebroids: All three structures seem to fit into a more general duality between subspaces of sections of the standard VB-Courant algebroid and brackets on vector bundles of the form T M ⊕ E ∗ , E → M a vector bundle. We establish a correspondence between certain properties of the brackets on one, and the subspaces on the other side.

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Hsu, Siu-fai, and 許紹輝. "Geometric quantization of fermions and complex bosons." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2013. http://hub.hku.hk/bib/B50434500.

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Geometric quantization is a subject of finding irreducible representations of certain group or algebra and identifying those equivalent representations by geometric means. Geometric quantization of even dimensional fermionic system has been constructed based on the spinor representation of even dimensional Clifford algebras. Although geometric quantization of odd dimensional fermionic system has not been done, the existence of spinor representations in odd dimension indicates that the geometric quantization is possible. In quantum field theory, charge conjungation can be defined on complex bosons and fermions. Without interaction, the particles and anti-particles essentially have same physical properties. In this thesis, we will first recall the setup of geometric quantization of even dimensional fermion and bosons. Then we will show how to quantize odd dimensional fermion. After that, charge conjungation on complex fermion and boson will be defined and the remaining effort will be put on how to identify the Hilbert spaces produced by different charge conjungations.
published_or_final_version
Mathematics
Master
Master of Philosophy

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Ugail, Hassan. "Time-dependent shape parameterisation of complex geometry using PDE surfaces." Nashboro Press, 2004. http://hdl.handle.net/10454/2686.

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Alves, Leonardo Soriani 1991. "Geometria complexa generalizada e tópicos relacionados." [s.n.], 2015. http://repositorio.unicamp.br/jspui/handle/REPOSIP/305829.

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Orientadores: Luiz Antonio Barrera San Martin, Lino Anderson da Silva Grama
Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matemática Estatística e Computação Científica
Made available in DSpace on 2018-08-27T10:27:44Z (GMT). No. of bitstreams: 1 Alves_LeonardoSoriani_M.pdf: 542116 bytes, checksum: b4db821b86b39eb2b221b4f63a4c9829 (MD5) Previous issue date: 2015
Resumo: Estudamos geometria complexa generalizada, que tem como casos particulares as geometrias complexa e simplética. Começamos com os seus fundamentos algébricos num espaço vetorial e transportamos essas noções para variedades. Estudamos o colchete de Courant na soma direta dos fibrados tangente e cotangente de uma variedade, que é essencial para definir a integrabilidade das estruturas complexas generalizadas. Verificamos que em nilvariedades de dimensão 6 sempre existe estrutura complexa generalizada invariante à esquerda, ainda que algumas delas não admitam estrutura complexa ou simplética. Estudamos duas noções de T-dualidade e suas relações com geometria complexa generalizada. Por fim recapitulamos a simetria do espelho para curvas elípticas e obtemos uma manifestação de simetria do espelho através de geometria complexa generalizada
Abstract: We study generalized complex geometry, which encompasses complex and symplectic geometry as particular cases. We begin with the algebraic basics on a vector space and then we transport these concepts to manifolds. We study the Courant bracket on the direct sum of tangent and cotangent bundles of a manifold, which is essential to define the integrability of the generalized complex structures. We check that on every $6$ dimensional nilmanifolds there is a left invariant generalized complex structure, even though some of them do not admit complex or symplectic structure. We study two notions of T-dualidade and its relations to generalized complex geometry. We recall mirror symmetry for elliptic curves and derive a manifestation of mirror symmetry from generalized complex geometry
Mestrado
Matematica
Mestre em Matemática

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Gabella, Maxime. "The AdS/CFT correspondence and generalized geometry." Thesis, University of Oxford, 2011. http://ora.ox.ac.uk/objects/uuid:6fd2037e-d0ec-4806-b4db-631eb3693071.

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The most general AdS$_5 imes Y$ solutions of type IIB string theory that are AdS/CFT dual to superconformal field theories in four dimensions can be fruitfully described in the language of generalized geometry, a powerful hybrid of complex and symplectic geometry. We show that the cone over the compact five-manifold $Y$ is generalized Calabi-Yau and carries a generalized holomorphic Killing vector field $xi$, dual to the R-symmetry. Remarkably, this cone always admits a symplectic structure, which descends to a contact structure on $Y$, with $xi$ as Reeb vector field. Moreover, the contact volumes of $Y$, which can be computed by localization, encode essential properties of the dual CFT, such as the central charge and the conformal dimensions of BPS operators corresponding to wrapped D3-branes. We then define a notion of ``generalized Sasakian geometry'', which can be characterized by a simple differential system of three symplectic forms on a four-dimensional transverse space. The correct Reeb vector field for an AdS$_5$ solution within a given family of generalized Sasakian manifolds can be determined---without the need of the explicit metric---by a variational procedure. The relevant functional to minimize is the type IIB supergravity action restricted to the space of generalized Sasakian manifolds, which turns out to be just the contact volume. We conjecture that this contact volume is equal to the inverse of the trial central charge whose maximization determines the R-symmetry of the dual superconformal field theory. The power of this volume minimization is illustrated by the calculation of the contact volumes for a new infinite family of solutions, in perfect agreement with the results of $a$-maximization in the dual mass-deformed generalized conifold theories.

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Ma, Yilin. "Nonlinear Calderón Problem on Stein Manifolds." Thesis, The University of Sydney, 2021. https://hdl.handle.net/2123/25757.

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This thesis is devoted to the study of inverse problems for semilinear elliptic equations on Stein manifolds with Kähler metric. After developing some preliminary techniques, we will show that the Dirichlet-Neumann maps for certain semilinear elliptic equations determine the nonlinearities. We will consider two inverse problems of this kind with distinct geometric conditions imposed. The first one is the inverse problem for nonlinear Schrödinger equations on Kähler manifolds having specific Stein-like properties. The second one is the inverse problem for nonlinear magnetic Schrödinger equations on Riemann surfaces with partial data boundary measurements. In both cases, the nonlinearities involved are assumed to have certain analytic representations and vanishing lower order terms. The key observation is that, by a suitable linearisation procedure, one could transform the nonlinear problems into series of linear problems which have close connections to the techniques we develop.

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LY, KIM HA. "ON TWO APPROACHES FOR PARTIAL DIFFERENTIAL EQUATIONS IN SEVERAL COMPLEX VARIABLES." Doctoral thesis, Università degli studi di Padova, 2014. http://hdl.handle.net/11577/3423534.

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The aim of this thesis is to present influence of notations of ''type" on partial differential equations in several complex variables. The notations of "type" here include the finite and the infinite type in the sense of Hormander, and D'Angelo. In particular, in the first part, under the finite type condition, we will consider the existence and uniqueness of solutions for the initial value problem associated to the heat operator δs+□b on CR manifolds. The finite type m is the critical condition to provide pointwise estimates of the heat kernel via theory of singular integral operators developed by E. Stein and A. Nagel, D.H. Phong and E. Stein. Next, in the second part, we will introduce a new method to investigate the Cauchy-Riemann equations δu = φ. The solutions are constructed via the integral representation method. Moreover, we will show that the new method here is also applied well to the complex Monge-Ampère operator (ddc)n inCn. The main point is that our method can pass some well-known results from the case of finite type to infinite type.
Lo scopo di questa tesi è quello di presentare l'influenza di notazioni di " tipo'' su equazioni differenziali alle derivate parziali in più variabili complesse. Le notazioni di "tipo" qui includono il finito e il tipo di infinito, nel senso di Hormander, e D'Angelo. In particolare, nella prima parte, a condizione tipo finito, prenderemo in considerazione l'esistenza e l'unicità delle soluzioni per il problema del valore iniziale associato ai operatore calore δs+□b su varietà CR. Il tipo finito m è la condizione fondamentale per fornire stime puntuali del nucleo del calore attraverso la teoria degli operatori integrali singolari sviluppate da E. Stein e A. Nagel, D.H. Phong e E. Stein. Prossimo, nella seconda parte, introdurremo un nuovo metodo per indagare la equazioni Cauchy-Riemann δu = φ. Le soluzioni sono costruite con via metodo rappresentazione integrale. Inoltre, mostreremo che il nuovo metodo qui viene applicato anche ben al complesso operatore Monge-Ampère (ddc)n inCn. Il punto principale è che il nostro metodo può passare alcuni risultati noti dal caso di tipo finito al tipo di infinito.

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Books on the topic "Complex Differential Geometry"

1

Kobayashi, Shoshichi. Complex differential geometry. 2nd ed. Basel: Birkhäuser, 1987.

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Ebeling, Wolfgang, Klaus Hulek, and Knut Smoczyk, eds. Complex and Differential Geometry. Berlin, Heidelberg: Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-20300-8.

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Siu, Yum Tong, ed. Complex differential geometry and nonlinear differential equations. Providence, Rhode Island: American Mathematical Society, 1986. http://dx.doi.org/10.1090/conm/049.

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Chavel, Isaac, and Hershel M. Farkas, eds. Differential Geometry and Complex Analysis. Berlin, Heidelberg: Springer Berlin Heidelberg, 1985. http://dx.doi.org/10.1007/978-3-642-69828-6.

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1943-, Greene Robert Everist, Yau Shing-Tung 1949-, and Summer Research Institute on Differential Geometry (1990 : University of California, Los Angeles), eds. Differential geometry. Providence, R.I: American Mathematical Society, 1993.

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Differential geometry of complex vector bundles. [Tokyo]: Iwanami Shoten, 1987.

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Summer Research Institute on Several Complex Variables and Complex Geometry (1989 University of California, Santa Cruz). Several complex variables and complex geometry. Edited by Bedford Eric 1947- and American Mathematical Society. Providence, R.I: American Mathematical Society, 1991.

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1946-, Carlson James A., Clemens C. Herbert 1939-, and Morrison David R. 1955-, eds. Complex geometry and Lie theory. Providence, R.I: American Mathematical Society, 1991.

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Chriss, Neil. Representation theory and complex geometry. Boston: Birkhäuser, 1997.

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Wells, Raymond O'Neil. Differential analysis on complex manifolds. 3rd ed. New York, NY : Springer-Verlag, 2010.

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Book chapters on the topic "Complex Differential Geometry"

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Greene, Robert E. "Complex differential geometry." In Lecture Notes in Mathematics, 228–88. Berlin, Heidelberg: Springer Berlin Heidelberg, 1987. http://dx.doi.org/10.1007/bfb0078614.

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Shiffman, Bernard, and Andrew John Sommese. "Complex Differential Geometry." In Vanishing Theorems on Complex Manifolds, 1–25. Boston, MA: Birkhäuser Boston, 1985. http://dx.doi.org/10.1007/978-1-4899-6680-3_1.

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Wells, Raymond O. "Differential Geometry." In Differential and Complex Geometry: Origins, Abstractions and Embeddings, 17–30. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-58184-2_2.

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Hess, Peter O., Mirko Schäfer, and Walter Greiner. "Pseudo-complex Differential Geometry." In Pseudo-Complex General Relativity, 217–45. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-25061-8_7.

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Merker, Joël. "Rationality in Differential Algebraic Geometry." In Complex Geometry and Dynamics, 157–209. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-20337-9_8.

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Bauer, Ingrid, Fabrizio Catanese, and Roberto Pignatelli. "Surfaces of general type with geometric genus zero: a survey." In Complex and Differential Geometry, 1–48. Berlin, Heidelberg: Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-20300-8_1.

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Kühnel, Marco. "Complete Kähler-Einstein manifolds." In Complex and Differential Geometry, 171–81. Berlin, Heidelberg: Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-20300-8_10.

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Kureš, Miroslav. "Fixed point subalgebras of Weil algebras: from geometric to algebraic questions." In Complex and Differential Geometry, 183–92. Berlin, Heidelberg: Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-20300-8_11.

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Lee, Yng-Ing. "Self-similar solutions and translating solutions." In Complex and Differential Geometry, 193–203. Berlin, Heidelberg: Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-20300-8_12.

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Leitner, Felipe. "Aspects of conformal holonomy." In Complex and Differential Geometry, 205–33. Berlin, Heidelberg: Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-20300-8_13.

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Conference papers on the topic "Complex Differential Geometry"

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Gilkey, Peter B., and Raina Ivanova. "Complex IP pseudo-Riemannian algebraic curvature tensors." In PDEs, Submanifolds and Affine Differential Geometry. Warsaw: Institute of Mathematics Polish Academy of Sciences, 2002. http://dx.doi.org/10.4064/bc57-0-13.

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Djorić, Mirjana, and Masafumi Okumura. "CR submanifolds of maximal CR dimension in complex manifolds." In PDEs, Submanifolds and Affine Differential Geometry. Warsaw: Institute of Mathematics Polish Academy of Sciences, 2002. http://dx.doi.org/10.4064/bc57-0-6.

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MATSUZOE, Hiroshi. "COMPLEX STATISTICAL MANIFOLDS AND COMPLEX AFFINE IMMERSIONS." In 4th International Colloquium on Differential Geometry and its Related Fields. WORLD SCIENTIFIC, 2015. http://dx.doi.org/10.1142/9789814719780_0012.

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Ryan, Patrick J. "INTRINSIC PROPERTIES OF REAL HYPERSURFACES IN COMPLEX SPACE FORMS." In Differential Geometry in Honor of Professor S S Chern. WORLD SCIENTIFIC, 2000. http://dx.doi.org/10.1142/9789812792051_0022.

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LI, SHI-JIE. "SUBMANIFOLDS WITH POINTWISE PLANAR NORMAL SECTIONS IN A COMPLEX PROJECTIVE SPACE." In Differential Geometry in Honor of Professor S S Chern. WORLD SCIENTIFIC, 2000. http://dx.doi.org/10.1142/9789812792051_0012.

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ANDO, Naoya. "COMPLEX CURVES AND ISOTROPIC MINIMAL SURFACES IN HYPERKÄHLER 4-MANIFOLDS." In 6th International Colloquium on Differential Geometry and its Related Fields. WORLD SCIENTIFIC, 2019. http://dx.doi.org/10.1142/9789811206696_0004.

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Dimiev, Stancho, and Kouei Sekigawa. "Topics in Complex Analysis, Differential Geometry and Mathematical Physics." In Third International Workshop on Complex Structures and Vector Fields. WORLD SCIENTIFIC, 1997. http://dx.doi.org/10.1142/9789814529518.

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ARVANITOYEORGOS, Andreas, Yusuke SAKANE, and Marina STATHA. "HOMOGENEOUS EINSTEIN METRICS ON COMPLEX STIEFEL MANIFOLDS AND SPECIAL UNITARY GROUPS." In 5th International Colloquium on Differential Geometry and its Related Fields. WORLD SCIENTIFIC, 2017. http://dx.doi.org/10.1142/9789813220911_0001.

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MAEDA, SADAHIRO, and TOSHIAKI ADACHI. "DIFFERENTIAL GEOMETRY OF CIRCLES IN A COMPLEX PROJECTIVE SPACE." In Proceedings of the Second Meeting. WORLD SCIENTIFIC, 2001. http://dx.doi.org/10.1142/9789812810038_0013.

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BAO, Tuya, and Toshiaki ADACHI. "EXTRINSIC SHAPES OF TRAJECTORIES ON REAL HYPERSURFACES OF TYPE (B) IN A COMPLEX HYPERBOLIC SPACE." In 6th International Colloquium on Differential Geometry and its Related Fields. WORLD SCIENTIFIC, 2019. http://dx.doi.org/10.1142/9789811206696_0012.

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Reports on the topic "Complex Differential Geometry"

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Snyder, Victor A., Dani Or, Amos Hadas, and S. Assouline. Characterization of Post-Tillage Soil Fragmentation and Rejoining Affecting Soil Pore Space Evolution and Transport Properties. United States Department of Agriculture, April 2002. http://dx.doi.org/10.32747/2002.7580670.bard.

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Tillage modifies soil structure, altering conditions for plant growth and transport processes through the soil. However, the resulting loose structure is unstable and susceptible to collapse due to aggregate fragmentation during wetting and drying cycles, and coalescense of moist aggregates by internal capillary forces and external compactive stresses. Presently, limited understanding of these complex processes often leads to consideration of the soil plow layer as a static porous medium. With the purpose of filling some of this knowledge gap, the objectives of this Project were to: 1) Identify and quantify the major factors causing breakdown of primary soil fragments produced by tillage into smaller secondary fragments; 2) Identify and quantify the. physical processes involved in the coalescence of primary and secondary fragments and surfaces of weakness; 3) Measure temporal changes in pore-size distributions and hydraulic properties of reconstructed aggregate beds as a function of specified initial conditions and wetting/drying events; and 4) Construct a process-based model of post-tillage changes in soil structural and hydraulic properties of the plow layer and validate it against field experiments. A dynamic theory of capillary-driven plastic deformation of adjoining aggregates was developed, where instantaneous rate of change in geometry of aggregates and inter-aggregate pores was related to current geometry of the solid-gas-liquid system and measured soil rheological functions. The theory and supporting data showed that consolidation of aggregate beds is largely an event-driven process, restricted to a fairly narrow range of soil water contents where capillary suction is great enough to generate coalescence but where soil mechanical strength is still low enough to allow plastic deforn1ation of aggregates. The theory was also used to explain effects of transient external loading on compaction of aggregate beds. A stochastic forInalism was developed for modeling soil pore space evolution, based on the Fokker Planck equation (FPE). Analytical solutions for the FPE were developed, with parameters which can be measured empirically or related to the mechanistic aggregate deformation model. Pre-existing results from field experiments were used to illustrate how the FPE formalism can be applied to field data. Fragmentation of soil clods after tillage was observed to be an event-driven (as opposed to continuous) process that occurred only during wetting, and only as clods approached the saturation point. The major mechanism of fragmentation of large aggregates seemed to be differential soil swelling behind the wetting front. Aggregate "explosion" due to air entrapment seemed limited to small aggregates wetted simultaneously over their entire surface. Breakdown of large aggregates from 11 clay soils during successive wetting and drying cycles produced fragment size distributions which differed primarily by a scale factor l (essentially equivalent to the Van Bavel mean weight diameter), so that evolution of fragment size distributions could be modeled in terms of changes in l. For a given number of wetting and drying cycles, l decreased systematically with increasing plasticity index. When air-dry soil clods were slightly weakened by a single wetting event, and then allowed to "age" for six weeks at constant high water content, drop-shatter resistance in aged relative to non-aged clods was found to increase in proportion to plasticity index. This seemed consistent with the rheological model, which predicts faster plastic coalescence around small voids and sharp cracks (with resulting soil strengthening) in soils with low resistance to plastic yield and flow. A new theory of crack growth in "idealized" elastoplastic materials was formulated, with potential application to soil fracture phenomena. The theory was preliminarily (and successfully) tested using carbon steel, a ductile material which closely approximates ideal elastoplastic behavior, and for which the necessary fracture data existed in the literature.

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