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Academic literature on the topic 'Codazzi tensor'

Author: Grafiati
Published: 9 March 2023
Last updated: 10 March 2023

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Journal articles on the topic "Codazzi tensor"

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Ali, Mohabbat, Abdul Haseeb, Fatemah Mofarreh, and Mohd Vasiulla. "Z-Symmetric Manifolds Admitting Schouten Tensor." Mathematics 10, no. 22 (November 16, 2022): 4293. http://dx.doi.org/10.3390/math10224293.

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The paper deals with the study of Z-symmetric manifolds (ZS)n admitting certain cases of Schouten tensor (specifically: Ricci-recurrent, cyclic parallel, Codazzi type and covariantly constant), and investigate some geometric and physical properties of the manifold. Moreover, we also study (ZS)4 spacetimes admitting Codazzi type Schouten tensor. Finally, we construct an example of (ZS)4 to verify our result.
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Ünal, İnan. "Generalized Quasi-Einstein Manifolds in Contact Geometry." Mathematics 8, no. 9 (September 16, 2020): 1592. http://dx.doi.org/10.3390/math8091592.

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In this study, we investigate generalized quasi-Einstein normal metric contact pair manifolds. Initially, we deal with the elementary properties and existence of generalized quasi-Einstein normal metric contact pair manifolds. Later, we explore the generalized quasi-constant curvature of normal metric contact pair manifolds. It is proved that a normal metric contact pair manifold with generalized quasi-constant curvature is a generalized quasi-Einstein manifold. Normal metric contact pair manifolds satisfying cyclic parallel Ricci tensor and the Codazzi type of Ricci tensor are considered, and further prove that a generalized quasi-Einstein normal metric contact pair manifold does not satisfy Codazzi type of Ricci tensor. Finally, we characterize normal metric contact pair manifolds satisfying certain curvature conditions related to M-projective, conformal, and concircular curvature tensors. We show that a normal metric contact pair manifold with generalized quasi-constant curvature is locally isometric to the Hopf manifold S2n+1(1)×S1.
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Stepanov, S., and I. Tsyganok. "Vanishing theorems for higher-order Killing and Codazzi." Differential Geometry of Manifolds of Figures, no. 50 (2019): 141–47. http://dx.doi.org/10.5922/0321-4796-2019-50-16.

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A Killing p-tensor (for an arbitrary natural number p ≥ 2) is a symmetric p-tensor with vanishing symmetrized covariant derivative. On the other hand, Codazzi p-tensor is a symmetric p-tensor with symmetric covariant derivative. Let M be a complete and simply connected Riemannian manifold of nonpositive (resp. non-negative) sectional curvature. In the first case we prove that an arbitrary symmetric traceless Killing p-tensor is parallel on M if its norm is a Lq -function for some q > 0. If in addition the volume of this manifold is infinite, then this tensor is equal to zero. In the second case we prove that an arbitrary traceless Codazzi p-tensor is equal to zero on a noncompact manifold M if its norm is a Lq -function for some q  1 .
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Calviño-Louzao, E., E. García-Río, J. Seoane-Bascoy, and R. Vázquez-Lorenzo. "Three-dimensional manifolds with special Cotton tensor." International Journal of Geometric Methods in Modern Physics 12, no. 01 (December 28, 2014): 1550005. http://dx.doi.org/10.1142/s021988781550005x.

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The Cotton tensor of three-dimensional Walker manifolds is investigated. A complete description of all locally conformally flat Walker three-manifolds is given, as well as that of Walker manifolds whose Cotton tensor is either a Codazzi or a Killing tensor.
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Mantica, Carlo Alberto, and Luca Guido Molinari. "Weyl compatible tensors." International Journal of Geometric Methods in Modern Physics 11, no. 08 (September 2014): 1450070. http://dx.doi.org/10.1142/s0219887814500704.

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We introduce the new algebraic property of Weyl compatibility for symmetric tensors and vectors. It is strictly related to Riemann compatibility, which generalizes the Codazzi condition while preserving much of its geometric implications. In particular, it is shown that the existence of a Weyl compatible vector implies that the Weyl tensor is algebraically special, and it is a necessary and sufficient condition for the magnetic part to vanish. Some theorems (Derdziński and Shen [11], Hall [15]) are extended to the broader hypothesis of Weyl or Riemann compatibility. Weyl compatibility includes conditions that were investigated in the literature of general relativity (as in McIntosh et al. [16, 17]). A simple example of Weyl compatible tensor is the Ricci tensor of an hypersurface in a manifold with constant curvature.
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MANTICA, CARLO ALBERTO, and YOUNG JIN SUH. "PSEUDO Z SYMMETRIC RIEMANNIAN MANIFOLDS WITH HARMONIC CURVATURE TENSORS." International Journal of Geometric Methods in Modern Physics 09, no. 01 (February 2012): 1250004. http://dx.doi.org/10.1142/s0219887812500041.

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In this paper we introduce a new notion of Z-tensor and a new kind of Riemannian manifold that generalize the concept of both pseudo Ricci symmetric manifold and pseudo projective Ricci symmetric manifold. Here the Z-tensor is a general notion of the Einstein gravitational tensor in General Relativity. Such a new class of manifolds with Z-tensor is named pseudoZ symmetric manifold and denoted by (PZS)n. Various properties of such an n-dimensional manifold are studied, especially focusing the cases with harmonic curvature tensors giving the conditions of closeness of the associated one-form. We study (PZS)n manifolds with harmonic conformal and quasi-conformal curvature tensor. We also show the closeness of the associated 1-form when the (PZS)n manifold becomes pseudo Ricci symmetric in the sense of Deszcz (see [A. Derdzinsky and C. L. Shen, Codazzi tensor fields, curvature and Pontryagin forms, Proc. London Math. Soc.47(3) (1983) 15–26; R. Deszcz, On pseudo symmetric spaces, Bull. Soc. Math. Belg. Ser. A44 (1992) 1–34]). Finally, we study some properties of (PZS)4 spacetime manifolds.
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Calvaruso, Giovanni. "Riemannian 3-metrics with a generic Codazzi Ricci tensor." Geometriae Dedicata 151, no. 1 (September 5, 2010): 259–67. http://dx.doi.org/10.1007/s10711-010-9532-5.

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Chen, Zhengmao. "A priori bounds and existence of smooth solutions to a $ L_p $ Aleksandrov problem for Codazzi tensor with log-convex measure." Electronic Research Archive 31, no. 2 (2022): 840–59. http://dx.doi.org/10.3934/era.2023042.

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<abstract><p>In the present paper, we prove the existence of smooth solutions to a $ L_p $ Aleksandrov problem for Codazzi tensor with a log-convex measure in compact Riemannian manifolds $ (M, g) $ with positive constant sectional curvature under suitable conditions. Our proof is based on the solvability of a Monge-Ampère equation on $ (M, g) $ via the method of continuity whose crucial factor is the a priori bounds of smooth solutions to the Monge-Ampère equation mentioned above. It is worth mentioning that our result can be seen as an extension of the classical $ L_p $ Aleksandrov problem in Euclidian space to the frame of Riemannian manifolds with weighted measures and that our result can also be seen as some attempts to get some new results on geometric analysis for Codazzi tensor.</p></abstract>
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Jelonek, Włodzimierz. "Characterization of affine ruled surfaces." Glasgow Mathematical Journal 39, no. 1 (January 1997): 17–20. http://dx.doi.org/10.1017/s0017089500031852.

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The aim of this paper is to give certain conditions characterizing ruled affine surfaces in terms of the Blaschke structure (∇, h, S) induced on a surface (M, f) in ℝ3. The investigation of affine ruled surfaces was started by W. Blaschke in the beginning of our century (see [1]). The description of affine ruled surfaces can be also found in the book [11], [3] and [7]. Ruled extremal surfaces are described in [9]. We show in the present paper that a shape operator S is a Codazzi tensor with respect to the Levi-Civita connection ∇ of affine metric h if and only if (M, f) is an affine sphere or a ruled surface. Affine surfaces with ∇S = 0 are described in [2] (see also [4]). We also show that a surface which is not an affine sphere is ruled iff im(S - HI) =ker(S - HI) and ket(S - HI) ⊂ ker dH. Finally we prove that an affine surface with indefinite affine metric is a ruled affine sphere if and only if the difference tensor K is a Codazzi tensor with respect to ∇.
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NAKAD, ROGER. "THE ENERGY-MOMENTUM TENSOR ON Spinc MANIFOLDS." International Journal of Geometric Methods in Modern Physics 08, no. 02 (March 2011): 345–65. http://dx.doi.org/10.1142/s0219887811005178.

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On Spinc manifolds, we study the Energy-Momentum tensor associated with a spinor field. First, we give a spinorial Gauss type formula for oriented hypersurfaces of a Spinc manifold. Using the notion of generalized cylinders, we derive the variational formula for the Dirac operator under metric deformation and point out that the Energy-Momentum tensor appears naturally as the second fundamental form of an isometric immersion. Finally, we show that generalized Spinc Killing spinors for Codazzi Energy-Momentum tensor are restrictions of parallel spinors.
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Dissertations / Theses on the topic "Codazzi tensor"

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ANSELLI, ANDREA. "PHI-CURVATURES, HARMONIC-EINSTEIN MANIFOLDS AND EINSTEIN-TYPE STRUCTURES." Doctoral thesis, Università degli Studi di Milano, 2020. http://hdl.handle.net/2434/703786.

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The aim of this thesis is to study the geometry of a Riemannian manifold M, with a special structure, called Einstein-type structure, depending on 3 real parameters, a smooth map phi into a target Riemannian manifold N, and a smooth function, called potential function, on M itself. We will occasionally let some of the parameters be smooth functions. The setting generalizes various previously studied situations:, Ricci solitons, almost Ricci-solitons, Ricci-harmonic solitons, quasi-Einstein manifolds and so on. By taking a constant potential function those structures reduces to harmonic-Einstein manifolds, that are a generalization of Einstein manifolds. The main ingredient of our analysis is the study of certain modified curvature tensors on M related to the map phi, called phi-curvatures, obtaining, for instance, their transformation laws under a conformal change of metric, and to develop a series of results for harmonic-Einstein manifolds that parallel those obtained for Einstein manifolds some times ago and also in the very recent literature. Einstein-type structures may be obtained, for some special values of the parameters involved, by a conformal deformation of a harmonic-Einstein manifold or even as the base of a warped product harmonic-Einstein manifold. The latter fact applies not only in the Riemannian but also in the Lorentzian setting and thus some Einstein-type structures are connected with solutions of the Einstein field equations, which are of particular interest in General Relativity. The main result of the thesis is the locally characterization, via a couple of integrability conditions and mild assumptions on the potential function, of Einstein-type structures with vanishing phi-Bach curvature (in the direction of the potential) as a warped product with harmonic-Einstein base and with an open real interval as fibre, extending in a very non trivial way a recent result for Bach flat Ricci solitons. Moreover the map phi depends only on the base of the warped product and not on the fibre . We also consider rigidity, triviality and non-existence results, both in the compact and non-compact cases. This is done via integral formulas and, in the non-compact case, via analytical tools, like the weak maximum principle and the classical results of Obata, Tashiro, Kanai.
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Conference papers on the topic "Codazzi tensor"

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Leder, J., A. Schwenk-Schellschmidt, U. Simon, and M. Wiehe. "Generating higher order Codazzi tensors by functions." In Geometry and Topology of Submanifolds IX. WORLD SCIENTIFIC, 1999. http://dx.doi.org/10.1142/9789812817976_0018.

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Libai, A. "On the Linear Intrinsic Dynamics of Thin Shells." In ASME 2001 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2001. http://dx.doi.org/10.1115/imece2001/ad-23754.

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Abstract Equations for the linear intrinsic dynamics of shells are presented and discussed. The variables in the proposed method are the six strain measures (½ × incremental metric and incremental curvature tensors of the reference surface). Two versions are presented. In the “compatibility version”, the field equations are: (a) expressions for the three extensional strain-accelerations in terms of the stress resultants and loads, and (b) the three incremental Gauss and Codazá-Mainardi compatibility equations of the reference surface. Constitutive relations are appended to complete the formulation. In the “rate version”, the field equations are expressions for the six strain-accelerations (extensional and bending) in terms of the stress-resultants and loads. Equivalence to the “compatibility version” is shown, provided that the initial conditions are satisfied. Two examples are given. In the first, specialization is made to the case of circular cylindrical shells. In the second, an inplane vibration problem of a rectangular plate is studied.
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