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.

In this work we prove that every locally symmetric smooth submanifoldM of Rn gives rise to a naturally defined smooth submanifold of the space of n × n symmetric matrices, called spectral manifold, consisting of all matrices whose ordered vector of eigenvalues belongs toM. We also present an explicit formula for the dimension of the spectral manifold in terms of the dimension and the intrinsic ...

We prove that if (M, g) is a compact locally irreducible Riemannian manifold with nonnegative isotropic curvature, then one of the following possibilities hold: (i) M admits a metric with positive isotropic curvature (ii) (M, g) is isometric to a locally symmetric space (iii) (M, g) is Kähler and biholomorphic to CP n. This is implied by the following two results: (i) Let (M, g) be a compact, l...

9 Abstract 10 We formulate two pairs of second order symmetric duality for nonlinear multiobjective mixed integer programs for 11 arbitrary cones. By using the concept of efficiency and second order invexity, we establish the weak, strong, converse 12 and self-duality theorems for our dual models. Several known results are obtained as special cases. 17 Following the earlier works of Dorn [5], D...