New rigidity results for a generalized Ricci-Hessian equation on manifolds.
problem Understanding rigidity in generalized Ricci-Hessian equations on manifolds.
method Proving new rigidity results related to a generalized Ricci-Hessian equation.
result New rigidity results for the generalized Ricci-Hessian equation on Riemannian manifolds.
The study explores special Ricci-Hessian equations on Kähler manifolds and identifies three types of solutions.
problem Exploring special Ricci-Hessian equations on Kähler manifolds.
method Using the Cartan-Kähler theorem and analyzing specific cases.
result Three types of solutions are identified for special Ricci-Hessian equations on Kähler manifolds.
Proves triviality and nonexistence of gradient Ricci solitons as warped metrics.
problem Proving triviality and nonexistence of gradient Ricci solitons as warped metrics.
method Proved through the construction of gradient Ricci solitons as warped products and studying Ricci-Hessian type manifolds.
result Gradient Ricci solitons are trivial and non-existent as warped metrics.
The paper classifies warped product almost Ricci solitons.
problem Understanding warped product almost Ricci solitons.
method Analyzing Ricci-Hessian type manifolds and considering two complementary cases.
result The vector field \(
abla\lambda\) belongs to the \(C^\infty(\Bbb{M})\)-module generated by \(
abla f\) and \(
abla\varphi\) in the first case.
On a manifold of dimension at least six, let (g,τ) be a pair consisting of a Kähler metric g which is locally Kähler irreducible, and a nonconstant smooth function τ. Off the zero set of τ, if the metric g^=g/τ2 is a gradient Ricci soliton which has soliton function 1/τ, we show that g^ is Kähler…
The study classifies Riemannian manifolds with specific Hessian properties.
problem Classifying Riemannian manifolds with a special Hessian structure.
method Analyzing manifolds with a non-identically vanishing function f whose Hessian is minus f times the Ricci tensor.
result Partial classification of manifolds with this Hessian structure.
We present the necessary and sufficient conditions for constructing gradient Ricci almost solitons that are realized as warped products. This will be done by means of Bishop-O'Neill's formulas and a particular study of Riemannian manifolds satisfying a Ricci-Hessian type equation. We prove existence results and give an…
Compact Riemannian manifolds with mostly positive curvature have finite fundamental groups.
problem Understanding conditions for finite fundamental groups in compact Riemannian manifolds.
method Using Bismut-Witten Laplacian and Ricci-Hessian inequalities.
result New conditions for finite fundamental groups in manifolds with mostly positive curvature.