Totally umbilical lightlike submanifolds

GCR-Lightlike Submanifolds of Indefinite Nearly Kaehler Manifolds

“…Then from (14), we obtain (42)ḡ(R(X,JX)Z,JZ) = − c 2 g(X, X)g(Z, Z) + 1 2 (∇ XJ )(Z) 2 for any X ∈ Γ(D 0 ) and Z ∈ Γ(JL 2 ). On the other hand, from (12) and (38) we have…”

GCR-Lightlike Submanifolds of a Semi-Riemannian Product Manifold

“…h * and A * are Γ(RadT M )-valued and Γ(S(T M ))-valued bilinear forms and are called as second fundamental forms of distributions S(T M ) and RadT M , respectively. Using (6) and (10), we obtain…”

The Axiom of Indefinite Surfaces in Semi-Riemannian Manifolds

“…We follow Duggal-Jin [3] for notations and results used in this paper. Throughout this paper we denote by F (M ) the algebra of smooth functions on M and by Γ(E) the F (M ) module of smooth sections of any vector bundle E over…”