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Integral formulas in riemannian geometry

In Honor of W. Kuperberg's 60th Birthday

In this article, first we prove that if a metric of a para-Sasakian manifold is a Ricci soliton, then either it is an Einstein (and V Killing) or a $$\eta $$-Einstein (and V leaves $$\varphi $$ invariant) manifold. Next, we prove that if a K-paracontact metric g is a gradient Ricci soliton, then it becomes a expanding soliton which is Einstein with constant scalar curvature. Further, we study the Ricci soliton where the potential vector field V is point wise collinear with the Reeb vector field on paracontact manifold. Finally, we consider the gradient Ricci soliton on $$(\kappa ,\mu )$$-paracontact manifold.

Ricci Solitons and Paracontact Geometry

We discuss the four-dimensional nonlinear sigma-model with an internalO(n) invariance coupled to the metric tensor field satisfying Einstein equations. We derive a bound on the coupling constant between the sigma-field and the metric tensor using the theory of harmonic maps. A special attention is paid to Einstein spaces and some new explicit solutions of the model are constructed.

Four-dimensional sigma-model coupled to the metric tensor field

Generalized weakly Ricci-symmetric ( CS)4 -spacetimes

Integral formulas of Minkowski type, involving the higher mean curvatures as multilinear forms on the normal bundle, are proved for compact oriented immersed submanifolds with arbitrary codimension in a Riemannian manifold of constant curvature, and as application a generalization of the Liebmann-Suss theorem as well as upper bounds for the first positive eigenvalue of the Laplace operator are given.

Integral formulas in riemannian geometry

Citations

In Honor of W. Kuperberg's 60th Birthday

Ricci Solitons and Paracontact Geometry

Four-dimensional sigma-model coupled to the metric tensor field

Generalized weakly Ricci-symmetric ( CS)4 -spacetimes

On integral formulas for submanifolds of spaces of constant curvature and some applications

Related Papers (5)

Riemannian Geometry of Contact and Symplectic Manifolds

The entropy formula for the Ricci flow and its geometric applications

Certain conditions for a Riemannian manifold to be isometric with a sphere

A class of almost contact riemannian manifolds

Curvature and Betti numbers