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.
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This work was supported by Grant No. 174012 of the Ministry of Education, Science and Technological Development of the Republic of Serbia. The authors are grateful to the anonymous referee for many valuable comments and suggestions that improved readability and overall presentation of the paper.
Communicated by Jost-Hinrich Eschenburg.
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This work was supported by Grant No. 174012 of the Ministry of Education, Science and Technological Development of the Republic of Serbia.
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Petrović, M.Z., Velimirović, L.S. A New Type of Generalized Para-Kähler Spaces and Holomorphically Projective Transformations. Bull. Iran. Math. Soc. 45, 1021–1043 (2019). https://doi.org/10.1007/s41980-018-0182-y
- Generalized Riemannian space
- Generalized para-Kähler space
- Curvature tensor
- Infinitesimal holomorphically projective transformation
Mathematics Subject Classification
- Primary 53B05
- Secondary 53B20