Spectral Geometry for Certain Noncompact Riemannian Manifolds.
Stability of slant and semi-slant submanifolds in Sasaki manifolds.
Standard homogeneous Einstein manifolds and Diophantine equations
Some new examples of standard homogeneous Einstein manifolds with semisimple transitive groups of motions and semisimple isotropy subgroups are constructed. For the construction of these examples the solutions of some systems of Diophantine equations are used.
Structures de Weyl-Einstein, espace de twisteurs et variétés de type S1 x S3.
Submanifolds of -structure manifold satisfying .
Submanifolds with harmonic mean curvature in pseudo-Hermitian geometry
We classify Hopf cylinders with proper mean curvature vector field in Sasakian 3-manifolds with respect to the Tanaka-Webster connection.
Sur les variétés presque sasakiennes
Symmetries and Kähler-Einstein metrics
We consider Fano manifolds that admit a collection of finite automorphism groups , such that the quotients are smooth Fano manifolds possessing a Kähler-Einstein metric. Under some numerical and smoothness assumptions on the ramification divisors, we prove that admits a Kähler-Einstein metric too.
Symplectic connections with parallel Ricci tensor
A variational principle introduced to select some symplectic connections leads to field equations which, in the case of the Levi Civita connection of Kähler manifolds, are equivalent to the condition that the Ricci tensor is parallel. This condition, which is stronger than the field equations, is studied in a purely symplectic framework.