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A new type of generalized para-Kähler spaces and holomorphically projective transformations. (English) Zbl 1421.53036

Summary: In the present paper, we define a new class of generalized para-Kähler spaces by using two different kinds of covariant derivatives. Some properties of the curvature tensors as well as those of the corresponding Ricci tensors of new generalized para-Kähler spaces are pointed out. Also, we consider some tensor fields that are invariant with respect to holomorphically projective mappings of generalized para-Kähler spaces. Finally, we examine some PDE systems for the existence of infinitesimal holomorphically projective transformations of new types of generalized para-Kähler spaces with parallel torsion.

MSC:

53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.)
53B05 Linear and affine connections
53B20 Local Riemannian geometry
53B35 Local differential geometry of Hermitian and Kählerian structures
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