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Abstract:
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In this dissertation, the classification of some important classes od hypersurfaces M
of the nearly Kähler S3 × S3 is considered, along with the parametrisation of the geodesic lines
of this manifold. This manifold is one of only four examples of homogeneous, 6-dimensional,
nearly Kähler manifolds. In addition to the almost complex structure J, this manifold is en-
dowed with an almost product structure P , which anticommutes with J. Owing to these facts,
there are two families of interesting tangent vector fields on S3 × S3, called P−singular vector
fields, having similar properties as A−singular vector fields on complex quadrics Q, which are
already known. The notion of P−principal and P−isotropic tangent vector fields of S3 × S3 is
defined, along with their basic properties. In the case of P−principal normal vector field ξ of
the hypersurface M , the partial classification is given, while the immersion of the hypersurfaces
M with P−isotropic normal vector field ξ is stated explicitly. |