/pdf/sasakian-ph-symmetric-spaces-dc1v1ytcbu.pdf

SASAKIAN φ -SYMMETRIC SPACES

Structures on differentiable manifolds have been very intensively studied in recent years both in differential topology as well as in differential geometry. Along with almost complex structures a systematic examination was begun of almost contact, affinor, symplectic, quaternion, and many other structures, a simple listing of which would take up considerable space. Not all of these structures are of equal value, but there is no doubt that the study of manifolds with various structures is of interest from both the global as well as the local point of view; moreover, for certain structures the possibility was outlined for applying them to various aspects of geometry and mechanics.

Structures On Differentiable Manifolds

/pdf/symmetries-and-phi-symmetric-spaces-zh3pwurhsg.pdf

Symmetries and $\phi$-symmetric spaces

A ϕ-symmetric spaceM is a complete connected regular Sasakian manifold, that fibers over an Hermitian symmetric spaceN, so that the geodesic involutions ofN lift to define global (involutive) automorphisms of the Sasakian structure onM. In the present paper the complete classification of ϕ-symmetric spaces is obtained. The groups of automorphisms of the Sasakian structures and the groups of isometries of the underlying Riemannian metrics are determined. As a corollary, the Sasakian space forms are also determined.

The classification of ϕ-symmetric Sasakian manifolds

We treat Killing-transversally symmetric spaces (briefly, KTS-spaces), that is, Riemannian manifolds equipped with a complete unit Killing vector field such that the reflections with respect to the flow lines of that field can be extended to global isometries. Such manifolds are homogeneous spaces equipped with a naturally reductive homogeneous structure and they provide a rich set of examples of reflection spaces. We prove that each simply connected reducible KTS-space M is a Riemannian product of a symmetric space AT and a special kind of KTS-space M", called a contact KTS-space. Such a particular manifold M" is an irreducible, odd-dimensional principal G1 -bundle over a Hermitian symmetric space. The main purpose of the paper is to give a classificationof thisspecial class of manifolds M".

/pdf/classification-of-killing-transversally-symmetric-spaces-1uil20nspt.pdf

Classification of Killing-transversally symmetric spaces

/pdf/a-study-on-certain-homogeneous-spaces-41gx4m1e4n.pdf

Kanji Motomiya

Papers

A study on certain homogeneous spaces