We have studied some geometric properties of conharmonically flat Sasakian manifold and an Einstein-Sasakian manifold satisfying R(X, Y ).N = 0. We have also obtained some results on special weakly Ricci symmetric Sasakian manifold and have shown that it is an Einstein manifold. AMS Mathematics Subject Classification (2000): 53C21, 53C25

In the Otsuki spaces use is made of two non-symmetric affine connection: one for contravariant and the other for covariant indices. In the present work we study the Ricci type identities for the basic differentiation and curvature tensors in these spaces. AMS Mathematics Subject Classification (2000): 53B05

Gu and Zhu [16] have shown that Type-II Ricci flow singularities develop from nongeneric rotationally symmetric Riemannian metrics on Sn+1 (n ≥ 2). In this paper, we describe and provide plausibility arguments for a detailed asymptotic profile and rate of curvature blow-up that we predict such solutions exhibit.

We show (a) that any entire graphic self-shrinking solution to the Lagrangian mean curvature flow in C with the Euclidean metric is flat; (b) that any space-like entire graphic self-shrinking solution to the Lagrangian mean curvature flow in C with the pseudo-Euclidean metric is flat if the Hessian of the potential is bounded below quadratically; and (c) the Hermitian counterpart of (b) for the...

In the Otsuki spaces one uses non-symmetric connections: one for contravariant and other for covariant indices. Also, we have two kinds of covariant differentiation-basic and non-basic. In the present work we investigate the Ricci type identities and curvature tensors for the non-basic differentiation.

We describe all almost contact metric, almost hermitian and G 2-structures admitting a connection with totally skew-symmetric torsion tensor, and prove that there exists at most one such connection. We investigate its torsion form, its Ricci tensor, the Dirac operator and the ∇-parallel spinors. In particular, we obtain solutions of the type II string equations in dimension n = 5, 6 and 7.

We find a kind of variations of Gauss-Codazzi-Ricci equations suitable for Kaluza-Klein reduction and Cauchy problem. Especially the counterpart of extrinsic curvature tensor has antisymmetric part as well as symmetric one. If the dependence of metric tensor on reduced dimensions is negligible it becomes a pure antisymmetric tensor. PACS:03.70;11.15

Riemannian and pseudo-Riemannian symmetric spaces with semisimple transvection group are known and classified for a long time. Contrary to that the description of pseudo-Riemannian symmetric spaces with non-semisimple transvection group is an open problem. In the last years some progress on this problem was achieved. In this article we want to explain these results and some of their applications.

We show that any non-Kähler, almost Kähler 4-manifold for which both the Ricci and the Weyl curvatures have the same algebraic symmetries as they have for a Kähler metric is locally isometric to the (only) proper 3-symmetric four-dimensional space. Mathematics Subject Classifications (2000): Primary 53B20, 53C25.

Some results on the properties of T -flat, quasiT -flat,  T -flat,  T -flat, T -semi-symmetric,  T Ricci recurrent and T - -recurrent LP-Sasakian manifolds are obtained. It is also proved that an LP-Sasakian manifold satisfying the condition T . 0 S  is an  -Einstein manifold. MSC 2000. 53C15, 53C25, 53C50, 53D15.