Rakesh Kumar Nagaich

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The index of a metric plays significant roles in differential geometry as it generates variety of vector fields such as space-like, time-like, and light-like fileds. With the help of these vector fields, we establish interesting properties on ( )-Sasakian manifolds, which was introduced by Bejancu and Duggal [1] and further investigated by Xufeng and Xiaoli(More)
A numerical method for solving second order, transient, parabolic partial differential equation is presented. The spatial discretization is based on Hermite collocation method (HCM). It is a combination of orthogonal collocation method and piecewise cubic Hermite interpolating polynomials. The solution is obtained in terms of cubic Hermite interpolating(More)
We have studied mixed foliate CR-lightlike submanifolds and CR-lightlike product of an indefinite Kaehler manifold and also obtained relationship between them. Mixed foliate CR-lightlike submanifold of indefinite complex space form has also been discussed and showed that the indefinite Kaehler manifold becomes the complex semi-Euclidean space.
We obtain the expressions for sectional curvature, holomorphic sectional curvature, and holomorphic bisectional curvature of a GCR-lightlike submanifold of an indefinite Kaehler manifold. We discuss the boundedness of holomorphic sectional curvature of GCR-lightlike submanifolds of an indefinite complex space form. We establish a condition for a(More)
In this paper we prove that there do not exist warped product GCR-lightlike submanifolds in the form M = N ⊥ × λ NT such that N ⊥ is an anti-invariant submanifold tangent to V and NT an invariant submanifold of ¯ M , other than GCR-lightlike product in an indefinite cosymplectic manifold. We also obtain some characterizations for a GCR-lightlike submanifold(More)
Copyright q 2012 Varun Jain et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. We define GCR-lightlike submanifolds of indefinite cosymplectic manifolds and give an example. Then, we study(More)
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