Abstract
A special type of anti-invariant Riemannian submersions is investigated. It is shown that the base space of an anti-invariant submersion is an almost contact metric manifold. The basic properties of these anti-invariant Riemannian submersions are presented. Some relations involving the Riemannian curvature invariants of these submersions are obtained.
REFERENCES
C. Altafini, ‘‘Redundant robotic chains on Riemannian submersions,’’ IEEE Trans. Robot. Autom. 20, 335–340 (2004).
R. Bhattacharya and V. Patrangenaru, ‘‘Nonparametic estimation of location and dispersion on Riemannian manifolds,’’ J. Stat. Plan. Inference 108, 23–35 (2002).
D. E. Blair, Riemannian Geometry of Contact and Symplectic Manifolds, Vol. 203 of Progress in Mathematics (Birkhäuser, Boston, MA, 2010).
M. Dominguez-Vázquez, ‘‘Real hypersurfaces with constant principal curvatures in complex space forms,’’ Differ. Geom. Appl. 29, S65–S70 (2011).
M. Falcitelli, S. Ianus, and A. M. Pastore, Riemannian Submersions and Related Topics (World Scientific, Singapore, 2004).
M. Falcitelli, A. M. Pastore, S. Ianus, and M. Visinescu, ‘‘Some applications of Riemannian submersions in physics,’’ Rom. J. Phys. 48, 627–639 (2003).
A. Gray, ‘‘Pseudo-Riemannian almost product manifolds and submersions,’’ J. Math. Mech. 16, 715–737 (1967).
M. Kon, ‘‘On a Hopf hypersurface of a complex space form,’’ Differ. Geom. Appl. 28, 295–300 (2010).
M. Kon, ‘‘Ricci tensor of real hypersurfaces,’’ Pacif. J. Math. 281, 103–123 (2016).
M. Kon, ‘‘Ricci tensor of Hopf hypersurfaces in a complex space form,’’ Int. Electron. J. Geom. 11, 1–7 (2018).
G. A. Lobos and M. Ortega, ‘‘Pseudo-parallel real hypersurfaces in complex space forms,’’ B. Korean Math. Soc. 41, 609–618 (2004).
M. Lohnherr and H. Reckziegel, ‘‘On ruled real hypersurfaces in complex space forms,’’ Geom. Dedic. 74, 267–286 (1999).
S. Maeda, ‘‘Ricci tensors of real hypersurfaces in a complex projective space,’’ Proc. Am. Math. Soc. 122, 1229–1235 (1994).
R. Niebergall and P. J. Ryan, ‘‘Real hypersurfaces in complex space forms,’’ Math. Sci. R. 32, 233–305 (1997).
B. O’Neill, ‘‘The fundamental equations of a submersion,’’ Mich. Math. J. 13, 459–469 (1966).
B. Şahin, ‘‘Anti-invariant Riemannian submersions from almost Hermitian manifolds,’’ Cent. Eur. J. Math. 8, 437–447 (2010).
B. Şahin, ‘‘Riemannian Submersions from almost Hermitian manifolds,’’ Taiwan. J. Math. 17, 629–659 (2013).
B. Şahin, Riemannian Submersions, Riemannian Maps in Hermitian Geometry, and their Applications (Academic, New York, 2017).
R. Takagi, ‘‘On homogeneous real hypersurfaces in a complex projective space,’’ Osaka J. Math. 10, 495–506 (1973).
Y. Tashiro and S. Tachibana, ‘‘On Fubinian and C-Fubinian manifolds,’’ Kodai Math. Sem. Rep. 15, 176–183 (1963).
H. Wang and W. Ziller, ‘‘Einstein metrics on principal torus bundles,’’ J. Differ. Geom. 31, 215–248 (1990).
B. Watson, ‘‘Almost Hermitian submersions,’’ J. Differ. Geom. 11, 147–165 (1976).
K. Yano and M. Kon, Structures on Manifolds, Vol. 3 of Series in Pure Mathematics (World Scientific, Singapore, 1984).
H. Zhao, A. R. Kelly, J. Zhou, J. Lu, and Y. Y. Yang, ‘‘Graph attribute embedding via Riemannian submersion learning,’’ Comput. Vis. Image Underst. 115, 962–975 (2011).
ACKNOWLEDGMENTS
The authors thank the editor and the anonymous reviewer for careful reading of the manuscript and helpful remarks.
Funding
This work was supported by ongoing institutional funding. No additional grants to carry out or direct this particular research were obtained.
Author information
Authors and Affiliations
Corresponding authors
Ethics declarations
The authors of this work declare that they have no conflicts of interest.
Additional information
Publisher’s Note.
Pleiades Publishing remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
(Submitted by M. A.Malakhaltsev)
Rights and permissions
About this article
Cite this article
Gülbahar, M., Erkan, E. & Maksut, F. A Special Type of Anti-invariant Riemannian Submersions. Lobachevskii J Math 44, 5231–5238 (2023). https://doi.org/10.1134/S1995080223120120
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S1995080223120120