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Continuum approximation of dislocation correlations for systems of curved dislocations. [PDF]

J Mater Sci Mater Theory
Marx AJ, Sandfeld S, Hochrainer T.
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On the P-Scalar Curvature

The Journal of Geometric Analysis, 2016
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Abedin, Farhan, Corvino, Justin
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On symmetric finsler spaces ofHp-scalar curvature and scalar curvature

Periodica Mathematica Hungarica, 1986
A Finsler space \(F_ n\) is said to be of Hp-scalar curvature if \(p\cdot H_{\ell ijr}=k(h_{\ell j} h_{ir}-h_{\ell r} h_{ij})\), where \(H_{\ell ijr}\) is the Berwald h-curvature tensor, p is an operator projecting on the indicatrix, \(h_{ij}\) is the angular metric tensor, and k is the curvature scalar.
Sinha, B. B., Ram, A.
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Prescribing Morse Scalar Curvatures

Milan Journal of Mathematics, 2022
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Prescribed scalar curvature on the $n$ -sphere

Calculus of Variations and Partial Differential Equations, 1996
The authors establish the Morse inequalities for the scalar curvature problem (i.e. The Kazdan-Warner problem) on \(S^3\). This result compliments an earlier existence theorem of \textit{A. Bahri} and \textit{J. M. Coron} [J. Funct. Anal. 95, No. 1, 106-172 (1991; Zbl 0722.53032)].
Schoen, Richard, Zhang, Dong
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S-Curvature, E-Curvature, and Berwald Scalar Curvature of Finsler Spaces

Differential Geometry and its Applications, 2023
This paper deals with the study of \(S\)-curvature, \(E\)-curvature and Berwald scalar curvature for Finsler spaces. More exactly, the author proves that the \(S\)-curvature of a Finsler space vanishes if and only if the \(E\)-curvature vanishes if and only if the Berwald scalar curvature vanishes.
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The Scalar Curvature

1976
We shall deal with some problems concerning the scalar curvature of compact riemannian manifolds. In particular we shall deal with the problem of Yamabe: Does there exist a conformal metric for which the scalar curvature is constant? And also problems posed by Chern, Nirenberg and others.
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Gap Extremality for Scalar Curvature

The Journal of Geometric Analysis
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Sun, Yukai, Wang, Changliang
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The Scalar Curvature on Totally Geodesic Fiberings

Annals of Global Analysis and Geometry, 2000
A compact Riemannian manifold \(N\) with scalar curvature \(\kappa _n\) is said to satisfy a comparison theorem for the scalar curvature iff for any other compact Riemannian manifold \(M\) (\(\dim M = \dim N\)) the inequality \(\kappa _M(x)\leq\kappa _N(f(x))\) holds at some \(x\in M\) whenever \(f:M\to N\) is a vector contracting spin map of non-zero ...
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Scalar curvature and hammocks

Mathematische Annalen, 1999
The author considers the generalization of the Gaussian curvature on an \(n\)-dimensional Riemannian manifold and the question of the deformation, i.e., the increase/decrease, of the scalar curvature which he calls the ``hammock effect''. Contents include the following sections: an introduction; singular conformal deformations; hammocks; curvature ...
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