arXiv subjects
Publications and source records attributed to Kouei Sekigawa.
We discuss two kinds of almost contact metric structures on a one-parameter family of totally umbilical hyperspheres in the nearly Kaehler unit 6-sphere.
We derive a curvature identity that holds on any 6-dimensional Riemannian manifold, from the Chern-Gauss-Bonnet theorem for a 6-dimensional closed Riemannian manifold. We also introduce some applications of this curvature identity.
We study curvature identities on contact metric manifolds on the geometry of the corresponding almost Käehler cones, and we provide applications of the derived curvature identities.
We discuss the integrability of orthogonal almost complex structures on Riemannian products of even-dimensional round spheres and give a partial answer to the question raised by E. Calabi concerning the existence of complex structures on a product manifold of a round 2-sphere and a round 4-sphere.
We show that any universal curvature identity which holds in the Riemannian setting extends naturally to the pseudo-Riemannian setting. Thus the Euh-Park-Sekigawa identity also holds for pseudo-Riemannian manifolds. We study the Euler-Lagrange equations associated to the Chern-Gauss-Bonnet formula and show that as in the Riemannian setting, they are given solely in terms of curvature (and not in terms of covariant derivatives of curvature) even in the pseudo-Riemannian setting.
We investigate the curvature properties of a two-parameter family of Hermitian structures on the product of two Sasakian manifolds, as well as intermediate relations. We give a necessary and sufficient condition for a Hermitian structure belonging to the family to be Einstein and provide concrete examples.
In this paper, a lot of examples of four-dimensional manifolds with an almost hypercomplex pseudo-Hermitian structure are constructed in several explicit ways. The received 4-manifolds are characterized by their linear invariants in the known aspects.