On a constant curvature statistical manifold

Conformal Curvature Flows on Compact Manifold of Negative Yamabe Constant

Abstract. We study some conformal curvature flows related to prescribed curvature problems on a smooth compact Riemannian manifold (M, g0) with or without boundary, which is of negative (generalized) Yamabe constant, including scalar curvature flow and conformal mean curvature flow. Using such flows, we show that there exists a unique conformal metric of g0 such that its scalar curvature in the...

Hypersurfaces with Constant Mean Curvature in a Lorentzian Space Form

On the maximal spacelike submanifolds of a pseudo- Riemannian quasi constant curvature manifold

In this paper, we first give a definition of pseudo-Riemannian quasi constant curvature manifold and then generalize T.Ishihara’s results. Mathematics Subject Classification: 53C42.

A note on curvature of α-connections of a statistical manifold

The family of α-connections ∇(α) on a statistical manifold M equipped with a pair of conjugate connections ∇ ≡ ∇(1) and ∇∗ ≡ ∇(−1) is given as ∇(α) = 1+α 2 ∇ + 1−α 2 ∇∗. Here, we develop an expression of curvature R for ∇(α) in relation to those for ∇,∇∗. Immediately evident from it is that ∇(α) is equiaffine for any α ∈ R when ∇,∇∗ are dually flat, as previously observed in Takeuchi and Amari ...

A Metric of Constant Curvature on Polycycles

We prove the following main theorem of the theory of (r, q)-polycycles. Suppose a nonseparable plane graph satisfies the following two conditions: (1) each internal face is an r-gon, where r ≥ 3 ; (2) the degree of each internal vertex is q , where q ≥ 3 , and the degree of each boundary vertex is at most q and at least 2 . Then it also possesses the following third property: (3) the vertices, ...