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 GCR-lightlike submanifold of an indefinite comple...

Let D = A + λB be the para-Blaschke tensor of the immersion x, where λ is a constant, A and B are the Blaschke tensor and the Möbius second fundamental form of x. A hypersurface x : M 7→ S(1) in the unit sphere S(1) without umbilical points is called a para-Blaschke isoparametric hypersurface if the Möbius form Φ vanishes identically and all of its para-Blaschke eigenvalues are constants. In [1...

In this paper, we study the precise asymptotics of noncompact Type-IIb solutions to mean curvature flow. Precisely, for each real number $\gamma >0$, construct flow solutions, in rotationally symmetric class, with following as $t\nearrow \infty$: (1) The highest concentrates at tip hypersurface (an umbilical point) and blows up rate $(2t+1)^{(\gamma -1)/2}$. (2) a neighbourhood tip, rescaling s...

In this paper, the geometry of F -invariant CR-submanifolds of a Kaehlerian product manifold is studied. Fundamental properties of this type submanifolds are investigated such as CR-product, D⊥-totally geodesic and mixed geodesic submanifold. Finally, we have researched totally-umbilical F -invariant proper CR-submanifolds and CR-products in a Kaehlerian product manifold M = M1(c1)×M2(c2) M.S.C...

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 necessary and sufficient conditions for a GCR...

An action describing the dynamics of an infinite collection of massless integer spin fields with spin s = 0, 1, 2, 3, ..., ∞ corresponding to totally symmetric Young tableaux representations of Poincare and anti-de Sitter groups is constructed, in any dimension d, in terms of two functions on a 2d-dimensional manifold. The action is represented by an integral localized on a 2d − 1-dimensional h...

We give a causal version of Eisenhart's geodesic characterization of Newtonian dynamics. We emphasize the geometric, coordinate independent properties needed to express Eisenhart's theorem in light of modern studies on the Bargmann structures (lightlike dimensional reduction). The construction of the space metric, Coriolis 1-form and scalar potential through which the theorem is formulated is s...