Real hypersurfaces with parallel Ricci tensor of a complex space form

Conformally Flat Normal Almost Contact 3-Manifolds

“…Let (M ; ϕ, ξ, η, g) be a cosymplectic 3-manifold. Differentiating (13) covariantly and using ∇ξ = 0 we get (14) (…”

“…In Section 5, we treat real hypersurfaces in a complex projective space or a complex hyperbolic space. Due to a result in [14], we know that there are no conformally flat real hypersurfaces in a non-flat complex space form M n+1 (c) (c = 0), n ≥ 2. Then, we show that a totally η-umbilical real hypersurface in P 2 C or H 2 C cannot be conformally flat (Proposition 5.6).…”

Ricci solitons on QR-hypersurfaces of a quaternionic space form ℚn

“…In [11], Ki proved that there are no real hypersurfaces with parallel Ricci tensor in a complex space form M n (c) with c = 0 when n ≥ 3. Kim [12] proved that when n = 2, this is also true.…”

Ricci tensors of real hypersurfaces in a complex projective space

“…Moreover, P"iC) in > 3) does not admit real hypersurfaces M with parallel Ricci tensor S (that is, VxS = 0 for each vector field X tangent to M, where V denotes the induced Riemannian connection from the Riemmanian connection V of P"(C) ; cf. [2]). So, it is natural to investigate real hypersurfaces M by using some conditions (on the derivative of S) which are weaker than VS = 0.…”