Quasi hemi-slant pseudo-Riemannian submersions in para-complex geometry
Yıl 2023,
Cilt: 72 Sayı: 4, 959 - 975, 29.12.2023
Esra Başarır Noyan
,
Yılmaz Gündüzalp
Öz
We introduce a new class of pseudo-Riemannian submersions which are called quasi hemi-slant pseudo-Riemannian submersions from para-Kaehler manifolds to pseudo-Riemannian manifolds as a natural generalization of slant submersions, semi-invariant submersions, semi-slant submersions and hemislant Riemannian submersions in our study. Also, we give non-trivial examples of such submersions. Further, some geometric properties with two types of quasi hemi-slant pseudo-Riemannian submersions are investigated
Kaynakça
- Akyol, M. A., Şahin, B., Conformal slant submersions, Hacettepe Journal of Mathematics and Statistics, 48(1) (2019), 28-44. https://doi.org/10.15672/HJMS.2017.506
- Akyol, M. A., Gündüzalp, Y., Semi-invariant semi-Riemannian submersions, Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 67(1) (2018), 80-92. https://doi.org/10.1501/Commua1\ 0000000832
- Alegre, P., Carriazo, A., Bi-slant submanifolds of para-Hermitian manifolds, Mathematics, 7(7) (2019), 618. https://doi.org/10.3390/math7070618
- Baditoiu, G., Ianus, S., Semi-Riemannian submersions from real and complex pseudo-hyperbolic spaces, Diff. Geom. and Appl., 16(1) (2002), 79-94. https://doi.org/10.1016/S0926-2245(01)00070-5
- Carriazo, A., Bi-slant immersions, Proc. ICRAMS 2000, (2000), 88-97.
- Falcitelli, M., Ianus, S., Pastore, A. M., Riemannian Submersions and Related Topics, World Scientific, 2004.
- Gündüzalp, Y., Slant submersions in paracontact geometry, Hacettepe Journal of Mathematics and Statistics, 49(2) (2020), 822-834. https://doi.org/10.15672/hujms.458085
- Gündüzalp, Y., Anti-invariant semi-Riemannian submersions from almost para-Hermitian manifolds, Journal of Function Spaces and Applications, 2013 (2013). https://doi.org/10.1155/2013/720623
- Gündüzalp, Y., Anti-invariant Pseudo-Riemannian submersions and Clairaut submersions from Paracosymplectic manifolds, Mediterr. J. Math., 16 (2019), 1-18. https://doi.org/10.1007/s00009-019-1359-1
- Gündüzalp, Y., Neutral slant submersions in paracomplex geometry, Afrika Matematika, 32 (2021), 1095-1110. https://doi.org/10.1007/s13370-021-00884-8
- Gündüzalp, Y., Slant submersions from almost product Riemannian manifolds, Turkish Journal of Mathematics, 37(5) (2013), 863-873. https://doi.org/10.3906/mat-1205-64
- Gray, A., Pseudo-Riemannian almost product manifolds and submersions, J. Math. Mech., 16 (1967), 715-737.
- Ianus, S., Mazzocco, R., Vilcu, G. E., Riemannian submersions from quaternionic manifolds, Acta Appl. Math., 104 (2008), 83-89. https://doi.org/10.1007/s10440-008-9241-3
- Ianus, S., Vilcu, G. E., Voicu, R. C., Harmonic maps and Riemannian submersions between manifolds endowed with special structures, Banach Center Publications, 93 (2011), 277-288.
- Ivanov, S., Zamkovoy, S., Para-Hermitian and para-quaternionic manifolds, Diff. Geom. and Its Appl., 23 (2005), 205-234. https://doi.org/10.1016/j.difgeo.2005.06.002
- Lee, C. W., Lee, J. W., S¸ahin, B., Vilcu, G-E., Optimal inequalities for Riemannian maps and Riemannian submersions involving Casorati curvatures, Annali di Matematica, 200 (2021), 1277–1295. https://doi.org/10.1007/s10231-020-01037-7
- O’Neill, B., The fundamental equations of a submersion, Michigan Math. J., 13 (1966), 459–469. https://doi.org/10.1307/mmj/1028999604
- Özdemir, F., Sayar, C., Taştan, H. M., Semi-invariant submersions whose total manifolds are locally product Riemannian, Quaestiones Mathematicae, 40(7) (2017), 909-926. https://doi.org/10.2989/16073606.2017.1335657
- Sepet, S. A., Ergüt, M., Pointwise slant submersions from cosymplectic manifolds, Turkish Journal of Mathematics, 40(3) (2016), 582-593. https://doi.org/10.3906/mat-1503-98
- Prasad, R., Shukla, S. S., Kumar, S., On Quasi-bi-slant submersions, Mediterr. J. Math., 16 (2019), 1-18. https://doi.org/10.1007/s00009-019-1434-7
- Sayar, C., Akyol, M. A., Prasad, R., Bi-slant submersions in complex geometry, International Journal of Geometric Methods in Modern Physics, 17(04) (2020), 2050055. https://doi.org/10.1142/S0219887820500553
- Sari, R., Akyol, M. A., Hemi-slant $\xi$-Riemannian submersions in contact geometry, Filomat, 34(11) (2020), 3747-3758. https://doi.org/10.2298/FIL2011747S
- Şahin, B., Slant submersions from almost Hermitian manifolds, Bull. Math. Soc. Sci. Math. Roumanie Tome., 54(102) (2011), 93-105.
- Şahin, B., Anti-invariant Riemannian submersions from almost Hermitian manifolds, Central European J.Math., 8(3) (2010), 437-447. https://doi.org/10.2478/s11533-010-0023-6
- Şahin, B., Semi-invariant submersions from almost Hermitian manifold, Canadian Mathematical Bulletin, 56(1) (2013), 173-183. https://doi.org/10.4153/CMB-2011-144-8
- Şahin, B., Riemannian Submersions, Riemannian Maps in Hermitian Geometry, and Their Applications, Academic Press, 2017.
- Şahin, B., Riemannian submersions from almost Hermitian manifolds, Taiwanese J. Math., 17(2) (2013), 629-659. https://doi.org/10.11650/tjm.17.2013.2191
- Taştan, H. M., Şahin, B., Yanan, Ş., Hemi-slant submersions, Mediterr. J. Math., 13 (2016), 2171–2184. https://doi.org/10.1007/s00009-015-0602-7
- Vilcu, G. E., Almost product structures on statistical manifolds and para-Kahler like statistical submersions, Bulletin des Sciences Math´ematiques, 171 (2021), 103018. https://doi.org/10.1016/j.bulsci.2021.103018
- Watson, B., Almost Hermitian submersions, J. Differential Geom., 11 (1976), 147-165. https://doi.org/10.4310/jdg/1214433303
Yıl 2023,
Cilt: 72 Sayı: 4, 959 - 975, 29.12.2023
Esra Başarır Noyan
,
Yılmaz Gündüzalp
Kaynakça
- Akyol, M. A., Şahin, B., Conformal slant submersions, Hacettepe Journal of Mathematics and Statistics, 48(1) (2019), 28-44. https://doi.org/10.15672/HJMS.2017.506
- Akyol, M. A., Gündüzalp, Y., Semi-invariant semi-Riemannian submersions, Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 67(1) (2018), 80-92. https://doi.org/10.1501/Commua1\ 0000000832
- Alegre, P., Carriazo, A., Bi-slant submanifolds of para-Hermitian manifolds, Mathematics, 7(7) (2019), 618. https://doi.org/10.3390/math7070618
- Baditoiu, G., Ianus, S., Semi-Riemannian submersions from real and complex pseudo-hyperbolic spaces, Diff. Geom. and Appl., 16(1) (2002), 79-94. https://doi.org/10.1016/S0926-2245(01)00070-5
- Carriazo, A., Bi-slant immersions, Proc. ICRAMS 2000, (2000), 88-97.
- Falcitelli, M., Ianus, S., Pastore, A. M., Riemannian Submersions and Related Topics, World Scientific, 2004.
- Gündüzalp, Y., Slant submersions in paracontact geometry, Hacettepe Journal of Mathematics and Statistics, 49(2) (2020), 822-834. https://doi.org/10.15672/hujms.458085
- Gündüzalp, Y., Anti-invariant semi-Riemannian submersions from almost para-Hermitian manifolds, Journal of Function Spaces and Applications, 2013 (2013). https://doi.org/10.1155/2013/720623
- Gündüzalp, Y., Anti-invariant Pseudo-Riemannian submersions and Clairaut submersions from Paracosymplectic manifolds, Mediterr. J. Math., 16 (2019), 1-18. https://doi.org/10.1007/s00009-019-1359-1
- Gündüzalp, Y., Neutral slant submersions in paracomplex geometry, Afrika Matematika, 32 (2021), 1095-1110. https://doi.org/10.1007/s13370-021-00884-8
- Gündüzalp, Y., Slant submersions from almost product Riemannian manifolds, Turkish Journal of Mathematics, 37(5) (2013), 863-873. https://doi.org/10.3906/mat-1205-64
- Gray, A., Pseudo-Riemannian almost product manifolds and submersions, J. Math. Mech., 16 (1967), 715-737.
- Ianus, S., Mazzocco, R., Vilcu, G. E., Riemannian submersions from quaternionic manifolds, Acta Appl. Math., 104 (2008), 83-89. https://doi.org/10.1007/s10440-008-9241-3
- Ianus, S., Vilcu, G. E., Voicu, R. C., Harmonic maps and Riemannian submersions between manifolds endowed with special structures, Banach Center Publications, 93 (2011), 277-288.
- Ivanov, S., Zamkovoy, S., Para-Hermitian and para-quaternionic manifolds, Diff. Geom. and Its Appl., 23 (2005), 205-234. https://doi.org/10.1016/j.difgeo.2005.06.002
- Lee, C. W., Lee, J. W., S¸ahin, B., Vilcu, G-E., Optimal inequalities for Riemannian maps and Riemannian submersions involving Casorati curvatures, Annali di Matematica, 200 (2021), 1277–1295. https://doi.org/10.1007/s10231-020-01037-7
- O’Neill, B., The fundamental equations of a submersion, Michigan Math. J., 13 (1966), 459–469. https://doi.org/10.1307/mmj/1028999604
- Özdemir, F., Sayar, C., Taştan, H. M., Semi-invariant submersions whose total manifolds are locally product Riemannian, Quaestiones Mathematicae, 40(7) (2017), 909-926. https://doi.org/10.2989/16073606.2017.1335657
- Sepet, S. A., Ergüt, M., Pointwise slant submersions from cosymplectic manifolds, Turkish Journal of Mathematics, 40(3) (2016), 582-593. https://doi.org/10.3906/mat-1503-98
- Prasad, R., Shukla, S. S., Kumar, S., On Quasi-bi-slant submersions, Mediterr. J. Math., 16 (2019), 1-18. https://doi.org/10.1007/s00009-019-1434-7
- Sayar, C., Akyol, M. A., Prasad, R., Bi-slant submersions in complex geometry, International Journal of Geometric Methods in Modern Physics, 17(04) (2020), 2050055. https://doi.org/10.1142/S0219887820500553
- Sari, R., Akyol, M. A., Hemi-slant $\xi$-Riemannian submersions in contact geometry, Filomat, 34(11) (2020), 3747-3758. https://doi.org/10.2298/FIL2011747S
- Şahin, B., Slant submersions from almost Hermitian manifolds, Bull. Math. Soc. Sci. Math. Roumanie Tome., 54(102) (2011), 93-105.
- Şahin, B., Anti-invariant Riemannian submersions from almost Hermitian manifolds, Central European J.Math., 8(3) (2010), 437-447. https://doi.org/10.2478/s11533-010-0023-6
- Şahin, B., Semi-invariant submersions from almost Hermitian manifold, Canadian Mathematical Bulletin, 56(1) (2013), 173-183. https://doi.org/10.4153/CMB-2011-144-8
- Şahin, B., Riemannian Submersions, Riemannian Maps in Hermitian Geometry, and Their Applications, Academic Press, 2017.
- Şahin, B., Riemannian submersions from almost Hermitian manifolds, Taiwanese J. Math., 17(2) (2013), 629-659. https://doi.org/10.11650/tjm.17.2013.2191
- Taştan, H. M., Şahin, B., Yanan, Ş., Hemi-slant submersions, Mediterr. J. Math., 13 (2016), 2171–2184. https://doi.org/10.1007/s00009-015-0602-7
- Vilcu, G. E., Almost product structures on statistical manifolds and para-Kahler like statistical submersions, Bulletin des Sciences Math´ematiques, 171 (2021), 103018. https://doi.org/10.1016/j.bulsci.2021.103018
- Watson, B., Almost Hermitian submersions, J. Differential Geom., 11 (1976), 147-165. https://doi.org/10.4310/jdg/1214433303