Results 31 to 40 of about 693,970 (340)
On Gromov’s scalar curvature conjecture [PDF]
Proceedings of the American Mathematical Society, 2009 We prove the Gromov conjecture on the macroscopic dimension of the universal covering of a closed spin manifold with a positive scalar curvature under the following assumptions on the fundamental group.0.10.1.Theorem.Suppose that a discrete groupπ\pihas the following properties:11. The Strong Novikov Conjecture holds forπ\pi.22.
Bolotov, Dmitry, Dranishnikov, Alexander
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Geodesic mappings of quasi-Einstein spaces with a constant scalar curvature
, 2020 V. A. Kiosak, G. V. Kovalova. Geodesic mappings of quasi-Einstein spaces with a constant scalar curvature, Mat. Stud. 53 (2020), 212–217. In this paper we study a special type of pseudo-Riemannian spaces – quasi-Einstein spaces of constant scalar ...
V. Kiosak, G. Kovalova
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TOTAL SCALAR CURVATURE AND HARMONIC CURVATURE
Taiwanese Journal of Mathematics, 2014 On a compact n-dimensional manifold, it has been conjectured that a critical point metric of the total scalar curvature, restricted to the space of metrics with constant scalar curvature of unit volume, will be Einstein. This conjecture was proposed in 1984 by Besse, but has yet to be proved.
Yun, Gabjin +2 more
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Deformation of the Weighted Scalar Curvature
Symmetry, Integrability and Geometry: Methods and Applications, 2023 Inspired by the work of Fischer-Marsden [Duke Math. J. 42 (1975), 519-547], we study in this paper the deformation of the weighted scalar curvature. By studying the kernel of the formal $L_\phi^2$-adjoint for the linearization of the weighted scalar curvature, we prove several geometric results.
Ho, Pak Tung, Shin, Jinwoo
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Constrained deformations of positive scalar curvature metrics [PDF]
Journal of differential geometry, 2019 We present a series of results concerning the interplay between the scalar curvature of a manifold and the mean curvature of its boundary. In particular, we give a complete topological characterization of those compact 3-manifolds that support Riemannian
A. Carlotto, Chao Li
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Kähler metrics with constant weighted scalar curvature and weighted K‐stability [PDF]
Proceedings of the London Mathematical Society, 2018 We introduce a notion of a Kähler metric with constant weighted scalar curvature on a compact Kähler manifold X , depending on a fixed real torus T in the reduced group of automorphisms of X , and two smooth (weight) functions v>0 and w , defined on the ...
Abdellah Lahdili
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Renormalizable Gravitational Action That Reduces to General Relativity on the Mass-Shell
Galaxies, 2018 We derive the equation that relates gravity to quantum mechanics: R|mass-shell=8πGc4LSM, where R is the scalar curvature, G is the gravitational constant, c is the speed of light and LSM is the Standard Model Lagrangian, or its future replacement ...
Peter D. Morley
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Geometric Inequalities for a Submanifold Equipped with Distributions
Mathematics, 2022 The article introduces invariants of a Riemannian manifold related to the mutual curvature of several pairwise orthogonal subspaces of a tangent bundle. In the case of one-dimensional subspaces, this curvature is equal to half the scalar curvature of the
Vladimir Rovenski
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Interior curvature estimates for hypersurfaces of prescribing scalar curvature in dimension three [PDF]
American Journal of Mathematics, 2019 :We prove a priori interior curvature estimates for hypersurfaces of prescribing scalar curvature equations in $\mathbb{R}^{3}$. The method is motivated by the integral method of Warren and Yuan.
Guohuan Qiu
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Scalar curvature, inequality and submanifold [PDF]
Proceedings of the American Mathematical Society, 1973 Using an inequality relation between scalar curvature and length of second fundamental form, we may conclude that a submanifold must have nonnegative (or positive) sectional curvatures. An application to compact submanifolds in obtained.
Chen, Bang-Yen, Okumura, Masafumi
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