O geometrii laplasiánu. I
Almost hermitian manifolds, whose Riemann curvature tensor satisfies an almost complex Bianchi-type identity, are considered. Some local and global theorems are proved. The special cases of parakähler manifolds and of Kähler manifolds are examined.
Quasi Einstein manifold is a simple and natural generalization of Einstein manifold. The object of the present paper is to study some properties of generalized quasi Einstein manifolds. We also discuss with space-matter tensor and some properties related to it. Two non-trivial examples have been constructed to prove the existence of generalized quasi Einstein spacetimes.
The object of the present paper is to introduce a non-flat Riemannian manifold called hyper-generalized recurrent manifolds and study its various geometric properties along with the existence of a proper example.
We prove that every generalized Cartan hypersurface satisfies the so called Roter type equation. Using this fact, we construct a particular class of generalized Robertson-Walker spacetimes.