This paper discusses the Norden golden manifold having a constant sectional curvature. First, it is shown that if has real curvature, flat. For this reason, notions of holomorphic-like curvature and bisectional on are investigated, but seen these do not work manifold. shows need for new concept In direction, notion (Norden curvature) proposed, an example given, constant, tensor field expressed ...

Let F : Σ n × [0, T) → R n+m be a family of compact immersed submanifolds moving by their mean curvature vectors. We show the Gauss maps γ : (Σ n , g t) → G(n, m) form a harmonic heat flow with respect to the time-dependent induced metric g t. This provides a more systematic approach to investigating higher codimension mean curvature flows. A direct consequence is any convex function on G(n, m)...

Let M be an n-dimensional submanifold in the simply connected space form F(c) with c + H > 0, where H is the mean curvature of M . We verify that if M(n ≥ 3) is an oriented compact submanifold with parallel mean curvature and its Ricci curvature satisfies RicM ≥ (n−2)(c+H2), then M is either a totally umbilic sphere, a Clifford hypersurface in an (n+1)-sphere with n = even, or CP ( 4 3 (c+H )) ...

The notion of general weighted Ricci curvatures appears naturally in many problems. N-Ricci curvature and the projective are just two special ones with totally different geometric meanings. In this paper, we study curvatures. We find that Randers metrics certain isotropic must have S-curvature. Then classify them via their navigation expressions. also equations characterize almost curvature.