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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)

- Rakesh Kumar, Jasleen Kaur, Rakesh Kumar Nagaich
- Int. J. Math. Mathematical Sciences
- 2011

The geometry of CR-submanifolds of Kaehler manifolds was initiated by Bejancu 1 and has been developed by 2–5 and others. They studied the geometry of CR-submanifolds with positive definite metric. Thus, this geometry may not be applicable to the other branches of mathematics and physics, where the metric is not necessarily definite. Moreover, because of… (More)

- HARI M. SRIVASTAVA, MANISH GOGNA, RAKESH KUMAR, R. K. NAGAICH
- 2010

In this paper, we consider totally umbilical CR-lightlike submanifolds of indefinite Kaehler manifolds and give a classification theorem for this.

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 M̄ , other than GCR-lightlike product in an indefinite cosymplectic manifold. We also obtain some characterizations for a GCR-lightlike submanifold to… (More)

- Rakesh Kumar, Rachna Rani, Rakesh Kumar Nagaich
- Int. J. Math. Mathematical Sciences
- 2007

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)

Copyright q 2011 Rakesh Kumar 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 study mixed geodesic GCR-lightlike submanifolds of indefinite Sasakian manifolds and obtain some… (More)

- Varun Jain, Rakesh Kumar, Rakesh Kumar Nagaich
- Int. J. Math. Mathematical Sciences
- 2012

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)

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)

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