On nearly Sasakian and nearly cosymplectic manifolds

Nearly Einstein Manifolds

The object of this paper is to define and study a new type of non-flat Riemannian manifold called nearly Einstein manifold. The notion of this nearly Einstein manifold has been established by an example and an existence theorem. Some geometric properties are obtained. AMS Mathematics Subject Classification (2010): 53C25.

A Geometric Inequality for Warped Product Semi-slant Submanifolds of Nearly Cosymplectic Manifolds

Recently, we have shown that there do not exist warped product semi-slant submanifolds of cosymplectic manifolds [K.A. Khan, V.A. Khan and Siraj Uddin, Balkan J. Geom. Appl. 13 (2008), 55–65]. The nearly cosymplectic structure generalizes the cosymplectic one. Therefore the nearly Kaehler structure generalizes the Kaehler structure in almost Hermitian setting. It is interesting that the warped ...

Hodge theory on nearly Kähler manifolds

Let (M, I,ω,Ω) be a nearly Kähler 6-manifold, that is, an SU(3)-manifold with the (3,0)-form Ω and the Hermitian form ω which satisfies dω = 3λReΩ, d ImΩ = −2λω, for a non-zero real constant λ. We develop an analogue of Kähler relations on M , proving several useful identities for various intrinsic Laplacians onM . WhenM is compact, these identities bring powerful results about cohomology of M ...

Simple Construction of a Frame which is $epsilon$-nearly Parseval and $epsilon$-nearly Unit Norm

In this paper, we will provide a simple method for starting with a given finite frame for an $n$-dimensional Hilbert space $mathcal{H}_n$ with nonzero elements and producing a frame which is $epsilon$-nearly Parseval and $epsilon$-nearly unit norm. Also, the concept of the $epsilon$-nearly equal frame operators for two given frames is presented. Moreover, we characterize all bounded invertible ...

Cr-submanifolds of a Nearly Trans-sasakian Manifold