Results 31 to 40 of about 1,470,963 (294)

On the differentiable sphere theorem for manifolds with Ricci curvatures bounded from above

Дифференциальная геометрия многообразий фигур
In the present paper, we prove that if is an -dimensional compact Riemannian manifold and if where , and are the sectional and Ricci curvatures of respectively, then is diffeomorphic to a spherical space form where is a finite group of ...
S. E. Stepanov, I. I. Tsyganok
doaj   +1 more source

Curvature Invariants for Statistical Submanifolds of Hessian Manifolds of Constant Hessian Curvature

Mathematics, 2018
We consider statistical submanifolds of Hessian manifolds of constant Hessian curvature. For such submanifolds we establish a Euler inequality and a Chen-Ricci inequality with respect to a sectional curvature of the ambient Hessian manifold.
Adela Mihai, Ion Mihai
doaj   +1 more source

The δ(2,2)-Invariant on Statistical Submanifolds in Hessian Manifolds of Constant Hessian Curvature

Entropy, 2020
We establish Chen inequality for the invariant δ ( 2 , 2 ) on statistical submanifolds in Hessian manifolds of constant Hessian curvature. Recently, in co-operation with Chen, we proved a Chen first inequality for such submanifolds.
Adela Mihai, Ion Mihai
doaj   +1 more source

On the Scalar Curvature and Sectional Curvatures of a Totally Real Submanifold [PDF]

Proceedings of the American Mathematical Society, 1975
For a totally real minimal submanifold of a complex space form, pinching for scalar curvature implies pinching for sectional curvatures.
openaire   +2 more sources

Mixed sectional-Ricci curvature obstructions on tori

, 2020
International audienceWe establish new obstruction results to the existence of Riemannian metrics on tori satisfying mixed bounds on both their sectional and Ricci curvatures.
Kloeckner, Benoît, Sabourau, Stéphane
core   +1 more source

Informational Holonomy Curvature and Its Discrete-to-Continuous Convergence

International Journal of Topology
We introduce a notion of curvature based on informational holonomy. Let (M,g) be a smooth Riemannian manifold and let π:P→M be a bundle of state spaces equipped fibrewise with a smooth divergence Dx inducing an information metric gPx.
David Gutierrez Ule
doaj   +1 more source

Bounds on Sectional Curvature and Interactions with Topology [PDF]

Jahresbericht der Deutschen Mathematiker-Vereinigung, 2020
AbstractIn this survey article we exemplarily illustrate implications of curvature assumptions on the topology of the underlying manifold. We shall mainly focus on sectional curvature and three different kinds of restrictions, namely on non-negative respectively on positive sectional curvature, as well as on two-sided curvature bounds.We shall see that
openaire   +2 more sources

Residual tail twisting in ascidian larvae is stabilized by asymmetric myofibrils that resist bilateral symmetry restoration

FEBS Letters, EarlyView.
Ascidian Ciona larvae initially show strong clockwise tail twisting, which is largely corrected during development. However, a small residual twist remains. This study shows that organized helical myofibrils in tail muscles mechanically stabilize this residual asymmetry, preventing complete restoration of bilateral symmetry and revealing how embryos ...
Yuki S. Kogure, Misaki K. Nishio, Satoru Okuda, Kohji Hotta   +3 more
wiley   +1 more source

The values of sectional curvature in indefinite metrics

Commentarii Mathematici Helvetici, 1979
exaly   +3 more sources

Sectional curvatures of K�hler moduli

Mathematische Annalen, 2004
We investigate a new property for compact Kahler manifolds. Let X be a Kahler manifold of dimension n and let H^{1,1} denote the (1,1) part of its real second cohomology. On this space, we have an degree n form given by cup product. Let K denote the open cone of Kahler classes in H^{1,1}, and K_1 the level set consisting of classes in K on which the n ...
openaire   +3 more sources