Conformal generic Riemannian maps from almost Hermitian manifolds

Abstract

In the present paper, we define the notion of conformal generic Riemannian maps from almost Hermitian manifolds onto Riemannian manifolds. We give examples for this type conformal maps. The concept of pluriharmonic map is used to get conditions defining totally geodesic foliations for certain distributions and being horizontally homothetic map on the base manifold.

Keywords

• Riemannian maps
• conformal Riemannian maps
• generic Riemannian maps
• conformal generic Riemannian maps

Kaynakça

1. Akyol MA. Generic Riemannian submersions from almost product Riemannian manifolds. Gazi University Journal of Science. 30, 2017, 89–100.
2. Ali S, Fatima T. Generic Riemannian submersions. Tamkang Journal of Mathematics. 44, 2013, 395–409.
3. Baird P, Wood JC. Harmonic Morphisms between Riemannian Manifolds. Oxford University Press, 2003.
4. Falcitelli M, Ianus S, Pastore AM. Riemannian Submersions and Related Topics. World Scientific, 2004.
5. Fischer AE. Riemannian maps between Riemannian manifolds. Contemporary Mathematics. 132, 1992, 331–366.
6. Gray A. Pseudo-Riemannian almost product manifolds and submersions. Journal of Applied Mathematics and Mechanics. 16, 1967, 715–737.
7. Miao J, Wang Y, Gu X, Yau ST. Optimal global conformal surface parametrization for visualization. Communications in Information and Systems. 4, 2005, 117–134.
8. Nore T. Second fundamental form of a map. Annali di Matematica Pura ed Applicata. 146, 1987, 281–310.

9. Ohnita Y. On pluriharmonicity of stable harmonic maps. Journal of the London Mathematical Society. 2, 1987, 563–587.
10. O’Neill B. The fundamental equations of a submersion. Michigan Mathematical Journal. 13, 1966, 458–469.
11. Sayar C, Taştan HM, Özdemir F, Tripathi MM. Generic submersions from Kaehler manifolds. Bulletin of the Malaysian Mathematical Sciences Society. 43, 2019, 809–831.
12. Şahin B. Riemannian submersions from almost Hermitian manifolds. Taiwanese Journal of Mathematics. 17, 2013, 629–659.
13. Şahin B. Riemannian Submersions, Riemannian Maps in Hermitian Geometry, and Their Applications. Academic Press, 2017.
14. Şahin B. Conformal Riemannian maps between Riemannian manifolds, their harmonicity and decomposition theorems. Acta Applicandae Mathematicae. 109, 2010, 829–847.
15. Şahin B. Generic Riemannian maps. Miskolc Mathematical Notes. 18, 2017, 453–467.
16. Şahin B, Yanan Ş. Conformal Riemannian maps from almost Hermitian manifolds. Turkish Journal of Mathematics. 42, 2018, 2436–2451.
17. Şahin B, Yanan Ş. Conformal semi-invariant Riemannian maps from almost Hermitian manifolds. Filomat. 33, 2019, 1125–1134.
18. Wang Y, Gu X, Yau ST. Volumetric harmonic map. Communications in Information and Systems. 3, 2003, 191–201.
19. Wang Y, Gu X, Chan TF, Thompson PM, Yau ST. Brain surface conformal parametrization with the Ricciflow. in: IEEE International Symposium on Biomedical Imaging-From nano to macro, Washington D.C., 2007, 1312–1315.
20. Watson B. Almost Hermitian submersions. Journal of Differential Geometry. 11, 1976, 147–165.
21. Yano K, Kon M. Structures on Manifolds. World Scientific, 1984.