191,738 research outputs found
Notes on Ricci solitons in -cosymplectic manifolds
The purpose of this article is to study an -cosymplectic manifold
admitting Ricci solitons. Here we consider mainly two classes of Ricci solitons
on -cosymplectic manifolds. One is the class of contact Ricci solitons. The
other is the class of gradient Ricci solitons, for which we give the local
classifications of . Meanwhile, we also give some properties of
-cosymplectic manifolds
Comparison Geometry for the Bakry-Emery Ricci Tensor
For Riemannian manifolds with a measure we prove mean
curvature and volume comparison results when the -Bakry-Emery Ricci
tensor is bounded from below and is bounded or is bounded
from below, generalizing the classical ones (i.e. when is constant). This
leads to extensions of many theorems for Ricci curvature bounded below to the
Bakry-Emery Ricci tensor. In particular, we give extensions of all of the major
comparison theorems when is bounded. Simple examples show the bound on
is necessary for these results.Comment: 21 pages, Some of the estimates have been improved. In light of some
new references, and to improve the exposition, the paper has been
reorganized. An appendix is also adde
Kinetic Scalar Curvature Extended Gravity
In this work we study a modified version of vacuum gravity with a
kinetic term which consists of the first derivatives of the Ricci scalar. We
develop the general formalism of this kinetic Ricci modified gravity and
we emphasize on cosmological applications for a spatially flat cosmological
background. By using the formalism of this theory, we investigate how it is
possible to realize various cosmological scenarios. Also we demonstrate that
this theoretical framework can be treated as a reconstruction method, in the
context of which it is possible to realize various exotic cosmologies for
ordinary Einstein-Hilbert action. Finally, we derive the scalar-tensor
counterpart theory of this kinetic Ricci modified gravity, and we show
the mathematical equivalence of the two theories.Comment: NPB Accepte
- …