Study of Slant Light like Submanifolds of Indefinite Almost Hermitian Manifolds

Abstract

The research work discussed in this thesis is concerned with the geometry newlineof Slant Lightlike Submanifolds of Indefinite Almost Hermitian Manifolds . newlineSemi-Riemannian geometry is the most natural and fruitful generalization newlineof Riemannian geometry. Since the second half of the 20th century, the Riemannian newlineand semi-Riemannian geometries have been active areas of research for geometers newlineand physicists. During the generalization of submanifold theory from Riemannian newlinemanifolds to semi-Riemannian manifolds, the induced metric on the submanifold newlinebecomes degenerate and gives rise to the class of lightlike submanifolds in the semi- newlineRiemannian category. In this case, the study becomes more difficult and strikingly newlinediand#8629;erent from the study of non-degenerate submanifolds as the intersection of normal newlinebundle and tangent bundle is non-empty. For this reason, the results obtained newlinefor non-degenerate submanifolds cannot be applied in the case of lightlike submanifolds. newlineOn the other hand, according to the behaviour of the tangent bundle of a submanifold newlinewith respect to the action of the almost complex structure J of the ambient newlinemanifold, there are two well known classes of submanifolds, namely, the complex newlinesubmanifolds and the totally real submanifolds. In other words, K is a complex newlinesubmanifold of an almost Hermitian manifold, if and only if, for any non-zero vector newlineY tangent to K at any point p 2 K, the angle between JY and the tangent plane newlineTpK is equal to zero, identically. On the other hand, K is a totally real submanifold newlineof an almost Hermitian manifold, if and only if, for any non-zero vector Y tangent newlineto K at any point p 2 K, the angle between JY and the tangent plane TpK is equal newlineto and#8673;/2, identically. Then, Chen [16] introduced a new class of submanifolds of an newlinealmost Hermitian manifold as a generalization of complex and totally real submanifolds, newlinecalled slant submanifolds. newline