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Автор: Grafiati

Опубліковано: 14 березня 2023

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Статті в журналах з теми "Submanifolds theory"

Jain, Varun, Amrinder Pal Singh, and Rakesh Kumar. "On the geometry of lightlike submanifolds of indefinite statistical manifolds." International Journal of Geometric Methods in Modern Physics 17, no. 07 (June 2020): 2050099. http://dx.doi.org/10.1142/s0219887820500991.

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We study lightlike submanifolds of indefinite statistical manifolds. Contrary to the classical theory of submanifolds of statistical manifolds, lightlike submanifolds of indefinite statistical manifolds need not to be statistical submanifold. Therefore, we obtain some conditions for a lightlike submanifold of indefinite statistical manifolds to be a lightlike statistical submanifold. We derive the expression of statistical sectional curvature and finally obtain some conditions for the induced statistical Ricci tensor on a lightlike submanifold of indefinite statistical manifolds to be symmetric.

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YANG, GUO-HONG, SHI-XIANG FENG, GUANG-JIONG NI, and YI-SHI DUAN. "RELATIONS OF TWO TRANSVERSAL SUBMANIFOLDS AND GLOBAL MANIFOLD." International Journal of Modern Physics A 16, no. 21 (August 20, 2001): 3535–51. http://dx.doi.org/10.1142/s0217751x01005080.

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In Riemann geometry, the relations of two transversal submanifolds and global manifold are discussed without any concrete models. By replacing the normal vector of a submanifold with the tangent vector of another submanifold, the metric tensors, Christoffel symbols and curvature tensors of the three manifolds are connected at the intersection points of the two submanifolds. When the inner product of the two tangent vectors of submanifolds vanishes, some corollaries of these relations give the most important second fundamental form and Gauss–Codazzi equation in the conventional submanifold theory. As a special case, the global manifold which is Euclidean is considered. It is pointed out that, in order to obtain the nonzero energy–momentum tensor of matter field in a submanifold, there must be the contributions of the above inner product and the other submanifold. Generally speaking, a submanifold is closely related to the matter fields of the other submanifold and the two submanifolds affect each other through the above inner product.

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MONTE, EDMUNDO M. "MATHEMATICAL SUPPORT TO BRANEWORLD THEORY." International Journal of Geometric Methods in Modern Physics 04, no. 08 (December 2007): 1259–67. http://dx.doi.org/10.1142/s0219887807002557.

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The braneworld theory appear with the purpose of solving the problem of the hierarchy of the fundamental interactions. The perspectives of the theory emerge as a new physics, for example, deviation of the law of Newton's gravity. One of the principles of the theory is to suppose that the braneworld is local submanifold in a space of high dimension, the bulk, solution of Einstein's equations in high dimension. In this paper we approach the mathematical consistency of this theory with a new proof of the fundamental theorem of submanifolds for the case of semi-Riemannian manifolds. This theorem consists of an essential mathematical support for this new theory. We find the integrability conditions for the existence of space–time submanifolds in a pseudo-Euclidean space.

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Wu, B. Y. "Some results on Finsler submanifolds." International Journal of Mathematics 27, no. 03 (March 2016): 1650021. http://dx.doi.org/10.1142/s0129167x1650021x.

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In this paper we study the submanifold theory in terms of Chern connection. We introduce the notions of the second fundamental form and mean curvature for Finsler submanifolds, and establish the fundamental equations by means of moving frame for the hypersurface case. We provide the estimation of image radius for compact submanifold, and prove that there exists no compact minimal submanifold in any complete noncompact and simply connected Finsler manifold with nonpositive flag curvature. We also characterize the Minkowski hyperplanes, Minkowski hyperspheres and Minkowski cylinders as the only hypersurfaces in Minkowski space with parallel second fundamental form.

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Varolin, Dror. "A Takayama-type extension theorem." Compositio Mathematica 144, no. 2 (March 2008): 522–40. http://dx.doi.org/10.1112/s0010437x07002989.

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AbstractWe prove a theorem on the extension of holomorphic sections of powers of adjoint bundles from submanifolds of complex codimension 1 having non-trivial normal bundle. The first such result, due to Takayama, considers the case where the canonical bundle is twisted by a line bundle that is a sum of a big and nef line bundle and a $\mathbb {Q}$-divisor that has Kawamata log terminal singularities on the submanifold from which extension occurs. In this paper we weaken the positivity assumptions on the twisting line bundle to what we believe to be the minimal positivity hypotheses. The main new idea is an L2 extension theorem of Ohsawa–Takegoshi type, in which twisted canonical sections are extended from submanifolds with non-trivial normal bundle.

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Ali, Akram, Wan Othman, and Sayyadah Qasem. "Geometric inequalities for CR-warped product submanifolds of locally conformal almost cosymplectic manifolds." Filomat 33, no. 3 (2019): 741–48. http://dx.doi.org/10.2298/fil1903741a.

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In this paper, we establish some inequalities for the squared norm of the second fundamental form and the warping function of warped product submanifolds in locally conformal almost cosymplectic manifolds with pointwise ?-sectional curvature. The equality cases are also considered. Moreover, we prove a triviality result for CR-warped product submanifold by using the integration theory on a compact orientate manifold without boundary.

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Biard, Séverine, and Emil J. Straube. "L2-Sobolev theory for the complex Green operator." International Journal of Mathematics 28, no. 09 (August 2017): 1740006. http://dx.doi.org/10.1142/s0129167x17400067.

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Анотація:

These notes are concerned with the [Formula: see text]-Sobolev theory of the complex Green operator on pseudoconvex, oriented, bounded and closed Cauchy–Riemann (CR)-submanifolds of [Formula: see text] of hypersurface type. This class of submanifolds generalizes that of boundaries of pseudoconvex domains. We first discuss briefly the CR-geometry of general CR-submanifolds and then specialize to this class. Next, we review the basic [Formula: see text]-theory of the tangential CR operator and the associated complex Green operator(s) on these submanifolds. After these preparations, we discuss recent results on compactness and regularity in Sobolev spaces of the complex Green operator(s).

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Urban, Zbyněk, and Ján Brajerčík. "The fundamental Lepage form in variational theory for submanifolds." International Journal of Geometric Methods in Modern Physics 15, no. 06 (May 8, 2018): 1850103. http://dx.doi.org/10.1142/s0219887818501037.

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The multiple-integral variational functionals for finite-dimensional immersed submanifolds are studied by means of the fundamental Lepage equivalent of a homogeneous Lagrangian, which can be regarded as a generalization of the well-known Hilbert form in the classical mechanics. The notion of a Lepage form is extended to manifolds of regular velocities and plays a basic role in formulation of the variational theory for submanifolds. The theory is illustrated on the minimal submanifolds problem, including analysis of conservation law equations.

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Mihai, Ion, and Radu-Ioan Mihai. "A New Algebraic Inequality and Some Applications in Submanifold Theory." Mathematics 9, no. 11 (May 23, 2021): 1175. http://dx.doi.org/10.3390/math9111175.

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We give a simple proof of the Chen inequality involving the Chen invariant δ(k) of submanifolds in Riemannian space forms. We derive Chen’s first inequality and the Chen–Ricci inequality. Additionally, we establish a corresponding inequality for statistical submanifolds.

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Urban, Zbyněk, and Demeter Krupka. "Foundations of higher-order variational theory on Grassmann fibrations." International Journal of Geometric Methods in Modern Physics 11, no. 07 (August 2014): 1460023. http://dx.doi.org/10.1142/s0219887814600238.

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A setting for higher-order global variational analysis on Grassmann fibrations is presented. The integral variational principles for one-dimensional immersed submanifolds are introduced by means of differential 1-forms with specific properties, similar to the Lepage forms from the variational calculus on fibred manifolds. Prolongations of immersions and vector fields to the Grassmann fibrations are defined as a geometric tool for the variations of immersions, and the first variation formula in the infinitesimal form is derived. Its consequences, the Euler–Lagrange equations for submanifolds and the Noether theorem on invariant variational functionals are proved. Examples clarifying the meaning of the Noether theorem in the context of variational principles for submanifolds are given.

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Дисертації з теми "Submanifolds theory"

Moore, Kimberley. "Deformation theory of Cayley submanifolds." Thesis, University of Cambridge, 2017. https://www.repository.cam.ac.uk/handle/1810/264801.

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Cayley submanifolds are naturally arising volume minimising submanifolds of $Spin(7)$- manifolds. In the special case that the ambient manifold is a four-dimensional Calabi--Yau manifold, a Cayley submanifold might be a complex surface, a special Lagrangian submanifold or neither. In this thesis, we study the deformation theory of Cayley submanifolds from two different perspectives.

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Vittone, Davide. "Submanifolds in Carnot groups." Doctoral thesis, Scuola Normale Superiore, 2006. http://hdl.handle.net/11384/85698.

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Ngo, Fabien. "Quantum structures of some non-monotone Lagrangian submanifolds." Doctoral thesis, Universite Libre de Bruxelles, 2010. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/210039.

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Анотація:

In this thesis we present a slight generalisation of the Pearl complex or relative quantum homology to some non monotone Lagrangian submanifolds. First we develop the theory for the so called almost monotone Lagrangian submanifolds, We apply it to uniruling problems as well as estimates for the relative Gromov width. In the second part we develop the theory for toric fiber in toric Fano manifolds, recovering previous computaional results of Floer homology .
Doctorat en Sciences
info:eu-repo/semantics/nonPublished

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Karlsson, Cecilia. "Orienting Moduli Spaces of Flow Trees for Symplectic Field Theory." Doctoral thesis, Uppsala universitet, Algebra och geometri, 2016. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-269551.

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This thesis consists of three scientific papers dealing with invariants of Legendrian and Lagrangian submanifolds. Besides the scientific papers, the thesis contains an introduction to contact and symplectic geometry, and a brief outline of Symplectic field theory with focus on Legendrian contact homology. In Paper I we give an orientation scheme for moduli spaces of rigid flow trees in Legendrian contact homology. The flow trees can be seen as the adiabatic limit of sequences of punctured pseudo-holomorphic disks with boundary on the Lagrangian projection of the Legendrian. So to equip the trees with orientations corresponds to orienting the determinant line bundle of the dbar-operator over the space of Lagrangian boundary conditions on the punctured disk. We define an orientation of this line bundle and prove that it is well-defined in the limit. We also prove that the chosen orientation scheme gives rise to a combinatorial algorithm for computing the orientation of the trees, and we give an explicit description of this algorithm. In Paper II we study exact Lagrangian cobordisms with cylindrical Legendrian ends, induced by Legendrian isotopies. We prove that the combinatorially defined DGA-morphisms used to prove invariance of Legendrian contact homology for Legendrian knots over the integers can be derived analytically. This is proved using the orientation scheme from Paper I together with a count of abstractly perturbed flow trees of the Lagrangian cobordisms. In Paper III we prove a flexibility result for closed, immersed Lagrangian submanifolds in the standard symplectic plane.

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Imagi, Yohsuke. "Surjectivity of a Gluing for Stable T2-cones in Special Lagrangian Geometry." 京都大学 (Kyoto University), 2014. http://hdl.handle.net/2433/189337.

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Donaldson, Neil Malcolm. "Symmetric R-spaces : a submanifold geometry and transformation theory." Thesis, University of Bath, 2005. https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.421253.

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Luo, Yong [Verfasser], and Guofang [Akademischer Betreuer] Wang. "Some topics from submanifold theory and geometric partial differential equations = Einige Themen aus Untermannigfaltigkeit Theorie und geometrischen partiellen Differentialgleichungen." Freiburg : Universität, 2013. http://d-nb.info/1114887412/34.

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Smith, Jack Edward. "Symmetry in monotone Lagrangian Floer theory." Thesis, University of Cambridge, 2017. https://www.repository.cam.ac.uk/handle/1810/267745.

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In this thesis we study the self-Floer theory of a monotone Lagrangian submanifold $L$ of a closed symplectic manifold $X$ in the presence of various kinds of symmetry. First we consider the group $\mathrm{Symp}(X, L)$ of symplectomorphisms of $X$ preserving $L$ setwise, and extend its action on the Oh spectral sequence to coefficients of arbitrary characteristic, working over an enriched Novikov ring. This imposes constraints on the differentials in the spectral sequence which force them to vanish in certain situations. We then specialise to the case where $L$ is $K$-homogeneous for a compact Lie group $K$, meaning roughly that $X$ is Kaehler, $K$ acts on $X$ by holomorphic automorphisms, and $L$ is a Lagrangian orbit. By studying holomorphic discs with boundary on $L$ we compute the image of low codimension $K$-invariant subvarieties of $X$ under the length zero closed-open string map. This places restrictions on the self-Floer cohomology of $L$ which generalise and refine the Auroux-Kontsevich-Seidel criterion. These often result in the need to work over fields of specific positive characteristics in order to obtain non-zero cohomology. The disc analysis is then developed further, with the introduction of the notion of poles and a reflection mechanism for completing holomorphic discs into spheres. This theory is applied to two main families of examples. The first is the collection of four Platonic Lagrangians in quasihomogeneous threefolds of $\mathrm{SL}(2, \mathbb{C})$, starting with the Chiang Lagrangian in $\mathbb{CP}^3$. These were previously studied by Evans and Lekili, who computed the self-Floer cohomology of the latter. We simplify their argument, which is based on an explicit construction of the Biran-Cornea pearl complex, and deal with the remaining three cases. The second is a family of $\mathrm{PSU}(n)$-homogeneous Lagrangians in products of projective spaces. Here the presence of both discrete and continuous symmetries leads to some unusual properties: in particular we obtain non-displaceable monotone Lagrangians which are narrow in a strong sense. We also discuss related examples including applications of Perutz's symplectic Gysin sequence and quilt functors. The thesis concludes with a discussion of directions for further research and a collection of technical appendices.

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Corni, Francesca. "Rectifiable sets and intrinsic Lipschitz graphs within Carnot Groups." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2017. http://amslaurea.unibo.it/13532/.

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A Carnot group is a connected, simply connected nilpotent Lie group whose Lie algebra is stratified. In these manifolds naturally arises a distance, called the Carnot-Caratheodory metric, that makes them sub-Riemannian manifolds. We define in Carnot groups homogeneous subgroups, complementary subgroups, intrinsic graphs, intrinsic Lipschitz graphs intrinsic differentiability and uniform intrinsic differentiability. We build two definitions of regular submanifolds in Carnot groups, that generalize the previous notions of H-regular surfaces and hypersurfaces. Then, we give two consequent notions of intrinsic rectifiable sets in Carnot groups and we prove their equivalence in groups of type *, as a consequence of a Rademacher's type, theorem for one codimensional intrinsic graphs.

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"Deformation theory of compact complex manifolds and CR manifolds." 2006. http://library.cuhk.edu.hk/record=b5896507.

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Анотація:

Ng Wai Man.
Thesis (M.Phil.)--Chinese University of Hong Kong, 2006.
Includes bibliographical references (leaves 87-88).
Abstracts in English and Chinese.
Chapter 1 --- Introduction --- p.1
Chapter 2 --- Infinitesimal Deformations for Compact Complex Manifolds --- p.4
Chapter 2.1 --- Differentiable Family --- p.4
Chapter 2.2 --- Local Triviality --- p.7
Chapter 2.3 --- Complex Analytic Family and Deformations --- p.10
Chapter 3 --- Existence Theorem --- p.15
Chapter 3.1 --- Obstructions as a Necessary Condition --- p.15
Chapter 3.2 --- The Existence Theorem --- p.16
Chapter 3.3 --- Convergence Proof --- p.21
Chapter 4 --- Completeness Theorem --- p.26
Chapter 4.1 --- The Completeness Theorem --- p.26
Chapter 4.2 --- Construction of Formal Power Series --- p.28
Chapter 4.3 --- Convergence Proof --- p.32
Chapter 4.4 --- Effective Parameters and Number of Moduli --- p.36
Chapter 4.5 --- Examples --- p.40
Chapter 5 --- CR Manifolds and Deformations --- p.42
Chapter 5.1 --- CR Submanifolds and Tangential Complex --- p.42
Chapter 5.2 --- Abstract CR Manifolds and its Cohomologies --- p.47
Chapter 5.3 --- Strongly Pseudoconvex Manifolds --- p.51
Chapter 5.4 --- Differentiable Family --- p.53
Chapter 6 --- Stability Theorems --- p.55
Chapter 6.1 --- Semi-continuity Theorem --- p.56
Chapter 6.1.1 --- The Case of Compact Complex Manifolds --- p.56
Chapter 6.1.2 --- The s.p.c. Compact CR Case --- p.63
Chapter 6.2 --- Other Stability Theorems for Complex Manifolds --- p.66
Chapter A --- The Complex Laplacian ´بa --- p.72
Chapter B --- Hodge-Dolbeault Theorem --- p.77
Chapter C --- Proof of Theorem 6.2 --- p.79
Chapter D --- Subelliptic Estimates of --- p.82
Bibliography --- p.87

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Книги з теми "Submanifolds theory"

Takao, Akahori, and Nihon Sūgakkai, eds. CR-geometry and overdetermined systems. Tokyo, Japan: Published for the Mathematical Society of Japan by Kinokuniya Co., 1997.

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Palais, Richard S. Critical point theory and submanifold geometry. Berlin: Springer-Verlag, 1988.

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E, Chang Der-chen, ed. Sub-Riemannian geometry: General theory and examples. Cambridge: Cambridge University Press, 2009.

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Dajczer, Marcos, and Ruy Tojeiro. Submanifold Theory. New York, NY: Springer US, 2019. http://dx.doi.org/10.1007/978-1-4939-9644-5.

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Palais, Richard S., and Chuu-liang Terng. Critical Point Theory and Submanifold Geometry. Berlin, Heidelberg: Springer Berlin Heidelberg, 1988. http://dx.doi.org/10.1007/bfb0087442.

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Li, Weiping, and Shihshu Walter Wei. Geometry and topology of submanifolds and currents: 2013 Midwest Geometry Conference, October 19, 2013, Oklahoma State University, Stillwater, Oklahoma : 2012 Midwest Geometry Conference, May 12-13, 2012, University of Oklahoma, Norman, Oklahoma. Providence, Rhode Island: American Mathematical Society, 2015.

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Georgia International Topology Conference (2009 University of Georgia). Low-dimensional and symplectic topology. Edited by Usher Michael 1978-. Providence, R.I: American Mathematical Society, 2011.

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(Dietmar), Salamon D., ed. J-holomorphic curves and symplectic topology. 2nd ed. Providence, R.I: American Mathematical Society, 2012.

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Ibragimov, Zair. Topics in several complex variables: First USA-Uzbekistan Conference on Analysis and Mathematical Physics, May 20-23, 2014, California State University, Fullerton, California. Providence, Rhode Island: American Mathematical Society, 2016.

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Southeast Geometry Seminar (15th 2009 University of Alabama at Birmingham). Geometric analysis, mathematical relativity, and nonlinear partial differential equations: Southeast Geometry Seminars Emory University, Georgia Institute of Technology, University of Alabama, Birmingham, and the University of Tennessee, 2009-2011. Edited by Ghomi Mohammad 1969-. Providence, Rhode Island: American Mathematical Society, 2013.

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Частини книг з теми "Submanifolds theory"

Palais, Richard S., and Chuu-liang Terng. "Isoparametric submanifolds." In Critical Point Theory and Submanifold Geometry, 106–39. Berlin, Heidelberg: Springer Berlin Heidelberg, 1988. http://dx.doi.org/10.1007/bfb0087448.

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Palais, Richard S., and Chuu-liang Terng. "Local geometry of submanifolds." In Critical Point Theory and Submanifold Geometry, 25–42. Berlin, Heidelberg: Springer Berlin Heidelberg, 1988. http://dx.doi.org/10.1007/bfb0087444.

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Palais, Richard S., and Chuu-liang Terng. "Topology of isoparametric submanifolds." In Critical Point Theory and Submanifold Geometry, 150–77. Berlin, Heidelberg: Springer Berlin Heidelberg, 1988. http://dx.doi.org/10.1007/bfb0087450.

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Furuhata, Hitoshi, and Izumi Hasegawa. "Submanifold Theory in Holomorphic Statistical Manifolds." In Geometry of Cauchy-Riemann Submanifolds, 179–215. Singapore: Springer Singapore, 2016. http://dx.doi.org/10.1007/978-981-10-0916-7_7.

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Bejancu, Aurel. "On the Theory of Finsler Submanifolds." In Finslerian Geometries, 111–29. Dordrecht: Springer Netherlands, 2000. http://dx.doi.org/10.1007/978-94-011-4235-9_11.

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Palais, Richard S., and Chuu-liang Terng. "Proper Fredholm submanifolds in Hilbert spaces." In Critical Point Theory and Submanifold Geometry, 140–49. Berlin, Heidelberg: Springer Berlin Heidelberg, 1988. http://dx.doi.org/10.1007/bfb0087449.

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Betounes, David. "Motion on a Submanifold." In Differential Equations: Theory and Applications, 463–540. New York, NY: Springer New York, 2001. http://dx.doi.org/10.1007/978-1-4757-4971-7_10.

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Palais, Richard S., and Chuu-liang Terng. "Elementary critical point theory." In Critical Point Theory and Submanifold Geometry, 181–222. Berlin, Heidelberg: Springer Berlin Heidelberg, 1988. http://dx.doi.org/10.1007/bfb0087451.

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Palais, Richard S., and Chuu-liang Terng. "Advanced critical point theory." In Critical Point Theory and Submanifold Geometry, 223–32. Berlin, Heidelberg: Springer Berlin Heidelberg, 1988. http://dx.doi.org/10.1007/bfb0087452.

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Palais, Richard S., and Chuu-liang Terng. "Preliminaries." In Critical Point Theory and Submanifold Geometry, 3–24. Berlin, Heidelberg: Springer Berlin Heidelberg, 1988. http://dx.doi.org/10.1007/bfb0087443.

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Тези доповідей конференцій з теми "Submanifolds theory"

Shapukov, Boris N. "Affinor structures in the oscillation theory." In PDEs, Submanifolds and Affine Differential Geometry. Warsaw: Institute of Mathematics Polish Academy of Sciences, 2002. http://dx.doi.org/10.4064/bc57-0-15.

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Dillen, Franki, Leopold Verstraelen, Luc Vrancken, and Ignace Van de Woestijne. "Geometry and Topology of Submanifolds, V." In Conferences on Differential Geometry and Vision & Theory of Submanifolds. WORLD SCIENTIFIC, 1993. http://dx.doi.org/10.1142/9789814535205.

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Powell, Nathan, and Andrew J. Kurdila. "Learning Theory for Estimation of Animal Motion Submanifolds." In 2020 59th IEEE Conference on Decision and Control (CDC). IEEE, 2020. http://dx.doi.org/10.1109/cdc42340.2020.9304243.

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Garaev, K. G. "ON THE PROBLEM OF MODIFIED THEORY OF INVARIANT VARIATION PROBLEMS CONSTRUCTION." In Geometry and Topology of Submanifolds IX. WORLD SCIENTIFIC, 1999. http://dx.doi.org/10.1142/9789812817976_0015.

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Canevari, Samuel, Guilherme Machado de Freitas, and Fernando Manfio. "A Survey on Submanifolds with Nonpositive Extrinsic Curvature." In International Workshop on Theory of Submanifolds 2016. Istanbul Teknik Üniversitesi: Istanbul Teknik Üniversitesi, 2017. http://dx.doi.org/10.24064/iwts2016.2017.11.

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Nistor, Simona, and Cezar Oniciuc. "Global Properties of Biconservative Surfaces in $\mathbb{R}^3$ and $\mathbb{S}^3$." In International Workshop on Theory of Submanifolds 2016. Istanbul Teknik Üniversitesi: Istanbul Teknik Üniversitesi, 2017. http://dx.doi.org/10.24064/iwts2016.2017.1.

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Gül, İlhan. "Quarter Symmetric Connections On Complex Weyl Manifolds." In International Workshop on Theory of Submanifolds 2016. Istanbul Teknik Üniversitesi: Istanbul Teknik Üniversitesi, 2017. http://dx.doi.org/10.24064/iwts2016.2017.10.

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Upadhyay, Abhitosh. "On the Shape Operator of Biconservative Hypersurfaces in $\mathbb E^5_2$." In International Workshop on Theory of Submanifolds 2016. Istanbul Teknik Üniversitesi: Istanbul Teknik Üniversitesi, 2017. http://dx.doi.org/10.24064/iwts2016.2017.12.

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Kahraman Aksoyak, Ferdağ, and Yusuf Yaylı. "Rotational Surfaces with Pointwise 1-Type Gauss Map in Pseudo Euclidean Space $\mathbb{E}_{2}^{4}$." In International Workshop on Theory of Submanifolds 2016. Istanbul Teknik Üniversitesi: Istanbul Teknik Üniversitesi, 2017. http://dx.doi.org/10.24064/iwts2016.2017.13.

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Özgür, Cihan. "On Slant Curves with pseudo-Hermitian $C$-parallel Mean Curvature Vector Fields." In International Workshop on Theory of Submanifolds 2016. Istanbul Teknik Üniversitesi: Istanbul Teknik Üniversitesi, 2017. http://dx.doi.org/10.24064/iwts2016.2017.14.

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