Rigidity of Holomorphically Projective Mappings of Kähler and Hyperbolic Kähler Spaces with Finite Complete Geodesics
Abstract
:1. Introduction
2. Kähler and Hyperbolic Kähler Spaces
3. General Questions Concerning Holomorphically Projective Mappings of Kähler and Hyperbolic Kähler Spaces
3.1. Definitions and the Basic Equations of Analytically Planar Curves on Kähler Spaces
3.2. Definitions and the Basic Equations of Holomorphically Projective Mappings
3.3. Holomorphically Projective Mappings and Killing Vector Fields
4. Holomorphically Projective Mappings of the Spaces
5. Rigidity of Kähler Spaces’ Respective Holomorphically Projective Mappings “in Whole”
5.1. Holomorphically Projective Mappings and Fundamental Functions Along Geodesics
5.2. HP Mappings with and Fundamental Functions Along Geodesics
- (a)
- If geodesic γ on is compact;
- (b)
- If geodesic γ on and its image on are complete;
- (c)
- If geodesic γ on is complete, and and .
5.3. Holomorphically Projective Mappings of [0] with n Complete Geodesics
5.4. Holomorphically Projective Mappings of [B] with Finite Complete Geodesics
6. Summary
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Mikeš, J.; Hinterleitner, I.; Peška, P.; Vítková, L. Rigidity of Holomorphically Projective Mappings of Kähler and Hyperbolic Kähler Spaces with Finite Complete Geodesics. Geometry 2025, 2, 3. https://doi.org/10.3390/geometry2010003
Mikeš J, Hinterleitner I, Peška P, Vítková L. Rigidity of Holomorphically Projective Mappings of Kähler and Hyperbolic Kähler Spaces with Finite Complete Geodesics. Geometry. 2025; 2(1):3. https://doi.org/10.3390/geometry2010003
Chicago/Turabian StyleMikeš, Josef, Irena Hinterleitner, Patrik Peška, and Lenka Vítková. 2025. "Rigidity of Holomorphically Projective Mappings of Kähler and Hyperbolic Kähler Spaces with Finite Complete Geodesics" Geometry 2, no. 1: 3. https://doi.org/10.3390/geometry2010003
APA StyleMikeš, J., Hinterleitner, I., Peška, P., & Vítková, L. (2025). Rigidity of Holomorphically Projective Mappings of Kähler and Hyperbolic Kähler Spaces with Finite Complete Geodesics. Geometry, 2(1), 3. https://doi.org/10.3390/geometry2010003