Hypersurfaces in spaces of constant curvature satisfying some Ricci-type equations

Abstract

Abstract. We investigate hypersurfaces M in semi-Riemannian spaces of constant curvature satisfying some Ricci-type equations and for which the tensor H 3 is a linear combination of the tensor H 2 , the second fundamental tensor H of M and the metric tensor g of M .

Hypersurfaces in space forms satisfying some generalized Einstein metric condition

“…where ψ and ρ are some functions on U H . We refer to [31,33,37,73,74,75,76,77] for results on hypersurfaces satisfying (1.17). Evidently, if M is a hypersurface in an 4-dimensional Riemannian space of constant curvature N 4 (c) then (1.17…”

Curvature properties of some class of minimal hypersurfaces in Euclidean spaces

“…Let M be a hypersurface in N n+1 s (c), n ≥ 4, satisfying (1) on U H . We define on U H the following functions ( [48], eq. (34)):…”

“…for some functions φ, ψ and ρ, were investigated in the following papers: [9]- [13], [17]- [18], [21]- [23], [25], [28]- [31], [33], [36], [40], [48]- [52]. The main results of Section 3 are presented in Proposition 3.1 and Theorem 3.2.…”

On curvature characterizations of some hypersurfaces in spaces of constant curvature

“…We mention that hypersurfaces M in N n+1 s (c), n 4, satisfying (1.4) and some curvature conditions, named Ricci-type equations, were recently investigated in [19].…”

“…Now using (4.3)(b), (4.3)(c), (4.13) and the identity κ = g ad S ad + 1 F g αδ S αδ we obtain (4.3)(d). (4.7) is a consequence of (19) and (34) of [4], (4.6)(a) and (4.6)(b) and the identity…”