Some Remarks on Quasi-Generalized CR-Null Geometry in Indefinite Nearly Cosymplectic Manifolds

Massamba, Fortuné; Ssekajja, Samuel

doi:10.1155/2016/9613182

Cited by 1 publication

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“…Some of the pioneering work on this topic is due to Duggal-Bejancu [3], Duggal-Sahin [4] and Kupeli [13]. It is upon those books that many other researchers, including but not limited to [2], [5], [6], [7], [8], [9], [10], [11], have extended their theories.…”

Section: Introductionmentioning

confidence: 99%

On total mean curvatures of foliated half-lightlike submanifolds in semi-Riemannian manifolds

Massamba

Ssekajja

2020

Hacettepe Journal of Mathematics and Statistics

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We derive total mean curvature integration formulae of a three co-dimensional foliation F n on a screen integrable half-lightlike submanifold, M n+1 in a semi-Riemannian manifold M n+3 . We give generalized differential equations relating to mean curvatures of a totally umbilical half-lightlike submanifold admitting a totally umbilical screen distribution, and show that they are generalizations of those given by [4].2010 Mathematics Subject Classification. Primary 53C25; Secondary 53C40, 53C50. Key words and phrases. Half-lightlike submanifolds; Newton transformation, foliation and mean curvature. FORTUNÉ MASSAMBA, SAMUEL SSEKAJJAProof. Replacing X with E in the Proposition 5.1 and then using (2.16) and (5.2) we obtain, for all r = 0, 1, · · · , n,from which the result follows by applying (5.4) and (5.5).Corollary 5.3. Under the hypothesis of Theorem 5.2, the induced connection ∇ on M is a metric connection, if and only if, the r-th mean curvature S r with respect to A N are solution of the following equationAlso the following holds. Corollary 5.4. Under the hypothesis of Theorem 5.2, M (c) is a semi-Euclidean space, if and only if, the r-th mean curvature S r with respect to A N are solution of the following equation E(S r+1 ) − τ (E)(r + 1)S r+1 = H 1 (r + 1)S r+1 .

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