Results 41 to 50 of about 13,851 (306)
On the transverse Scalar Curvature of a Compact Sasaki Manifold
Complex Manifolds, 2014 We show that the standard picture regarding the notion of stability of constant scalar curvature metrics in Kähler geometry described by S.K. Donaldson [10, 11], which involves the geometry of infinitedimensional groups and spaces, can be applied to the ...
He Weiyong
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On the scalar curvature and sectional curvatures of a Kaehler submanifold [PDF]
Proceedings of the American Mathematical Society, 1973 For a Kaehler submanifold of a complex space form, pinching for scalar curvature implies pinching for sectional curvatures. 1 . Statement of result. The scalar curvature is, by definition, the sum of Ricci curvatures with respect to an orthonormal basis of the tangent space, and the Ricci curvature is the sum of sectional curvatures.
Chen, Bang-Yen, Ogiue, Koichi
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The volume entropy of a surface decreases along the Ricci flow [PDF]
, 2004 The volume entropy, h(g), of a compact Riemannian manifold (M,g) measures the growth rate of the volume of a ball of radius R in its universal cover.
Manning, Anthony, ANTHONY MANNING
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Curvature operators and scalar curvature invariants [PDF]
Classical and Quantum Gravity, 2010 We continue the study of the question of when a pseudo-Riemannain manifold can be locally characterised by its scalar polynomial curvature invariants (constructed from the Riemann tensor and its covariant derivatives). We make further use of alignment theory and the bivector form of the Weyl operator in higher dimensions, and introduce the important ...
Hervik, Sigbjørn, Coley, Alan
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On the scalar curvature of complex surfaces [PDF]
Geometric and Functional Analysis, 1995 10 pages, LaTeX, with optional \Bbb font replaceable by ...
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Constant Scalar Curvature Metrics on Connected Sums
, 2001 The Yamabe problem (proved in 1984) guarantees the existence of a metric of constant scalar curvature in each conformal class of Riemannian metrics on a compact manifold of dimension $n \geq 3$, which minimizes the total scalar curvature of this ...
Joyce, D, Dominic Joyce, Joyce, Dominic
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Metric Inequalities with Scalar Curvature [PDF]
Geometric and Functional Analysis, 2018 We establish several inequalities for manifolds with positive scalar curvature and, more generally, for the scalar curvature bounded from below, in the spirit of the classical bound on the distances between conjugates points in surfaces with positive sectional curvature.
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On Square metrics of scalar flag curvature [PDF]
Israel Journal of Mathematics, 2018 We consider a special class of Finsler metrics --- square metrics which are defined by a Riemannian metric and a 1-form on a manifold. We show that an analogue of the Beltrami Theorem in Riemannian geometry is still true for square metrics in dimension $n\ge 3$, namely, an $n(\ge 3)$-dimensional square metric is locally projectively flat if and only if
Shen, Zhongmin, Yang, Guojun
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Positive Scalar Curvature and Applications [PDF]
, 2019 We introduce the idea of curvature, including how it developed historically, and focus on the scalar curvature of a manifold. A major current research topic involves understanding positive scalar curvature.
Wraith, David, Rosenberg, Jonathan
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On Sprays of Scalar Curvature and Metrizability
The Journal of Geometric Analysis, 2023 20 ...
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