Métriques d'Einstein-Kähler sur les variétés de Fano : obstructions et existence
Minimal dimensions for flat manifolds with prescribed holonomy.
Minimal Reeb vector fields on almost Kenmotsu manifolds
A necessary and sufficient condition for the Reeb vector field of a three dimensional non-Kenmotsu almost Kenmotsu manifold to be minimal is obtained. Using this result, we obtain some classifications of some types of -almost Kenmotsu manifolds. Also, we give some characterizations of the minimality of the Reeb vector fields of -almost Kenmotsu manifolds. In addition, we prove that the Reeb vector field of an almost Kenmotsu manifold with conformal Reeb foliation is minimal.
Minimal slant submanifolds of the smallest dimension in S-manifolds.
We study slant submanifolds of S-manifolds with the smallest dimension, specially minimal submanifolds and establish some relations between them and anti-invariant submanifolds in S-manifolds, similar to those ones proved by B.-Y. Chen for slant surfaces and totally real surfaces in Kaehler manifolds.
Mixed 3-Sasakian structures and curvature
We deal with two classes of mixed metric 3-structures, namely the mixed 3-Sasakian structures and the mixed metric 3-contact structures. First, we study some properties of the curvature of mixed 3-Sasakian structures. Then we prove the identity between the class of mixed 3-Sasakian structures and the class of mixed metric 3-contact structures.
Monopole metrics and the orbifold Yamabe problem
We consider the self-dual conformal classes on discovered by LeBrun. These depend upon a choice of points in hyperbolic -space, called monopole points. We investigate the limiting behavior of various constant scalar curvature metrics in these conformal classes as the points approach each other, or as the points tend to the boundary of hyperbolic space. There is a close connection to the orbifold Yamabe problem, which we show is not always solvable (in contrast to the case of compact manifolds)....
-quasi Einstein manifolds satisfying certain curvature conditions
Nearly Kähler and nearly parallel -structures on spheres
In some other context, the question was raised how many nearly Kähler structures exist on the sphere equipped with the standard Riemannian metric. In this short note, we prove that, up to isometry, there exists only one. This is a consequence of the description of the eigenspace to the eigenvalue of the Laplacian acting on -forms. A similar result concerning nearly parallel -structures on the round sphere holds, too. An alternative proof by Riemannian Killing spinors is also indicated.
New aspects on CR-structures of codimension 2 on hypersurfaces of Sasakian manifolds
We introduce a torsion free linear connection on a hypersurface in a Sasakian manifold on which we have defined in natural way a -structure of -codimension 2. We study the curvature properties of this connection and we give some interesting examples.
New Einstein metrics on which are non-naturally reductive
We prove that there are at least two new non-naturally reductive invariant Einstein metrics on . It implies that every compact simple Lie group ...
New examples of Einstein metrics in dimension four.
Non-compact cohomogeneity one Einstein manifolds
Non-existence of almost Kähler structure on hyperbolic spaces of dimension 2n(...4).
Non-existence of proper semi-invariant submanifolds of a Lorentzian para-Sasakian manifold.
Nonlinear elliptic equations on compact Riemannian manifolds and asymptotics of Emden equations.
Non-standard Einstein extensions of five dimensional nilpotent metric Lie algebras.
Nontrivial examples of coupled equations for Kähler metrics and Yang-Mills connections
We provide nontrivial examples of solutions to the system of coupled equations introduced by M. García-Fernández for the uniformization problem of a triple (M; L; E), where E is a holomorphic vector bundle over a polarized complex manifold (M, L), generalizing the notions of both constant scalar curvature Kähler metric and Hermitian-Einstein metric.
Normal form of the NK-curvature operators
Normal semi-invariant submanifolds of a Sasakian manifold
Normally flat semiparallel submanifolds in space forms as immersed semisymmetric Riemannian manifolds
By means of the bundle of orthonormal frames adapted to the submanifold as in the title an explicit exposition is given for these submanifolds. Two theorems give a full description of the semisymmetric Riemannian manifolds which can be immersed as such submanifolds. A conjecture is verified for this case that among manifolds of conullity two only the planar type (in the sense of Kowalski) is possible.