Existence and uniqueness theorems for pointwise-slant immersions in Sasakian space forms

Noura Alhouiti; Noura Alhouiti

doi:10.3934/math.2023892

AIMS Mathematics

2023, Volume 8, Issue 8: 17470-17483. doi: 10.3934/math.2023892

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Existence and uniqueness theorems for pointwise-slant immersions in Sasakian space forms

Noura Alhouiti ^,

Department of Mathematics, University Collage of Haqel, University of Tabuk, 71491 Tabuk, Saudi Arabia

Received: 24 February 2023 Revised: 20 April 2023 Accepted: 24 April 2023 Published: 19 May 2023
MSC : 53C25, 53C42

In this paper we derive the Existence and Uniqueness Theorems for pointwise slant immersions in Sasakian space forms which extend the Existence and Uniqueness Theorems for slant immersions in Sasakian space forms proved by Cabreizo et al in 2001.
- Sasakian manfold,
- sectional curvature,
- pointwise-slant immersion
Citation: Noura Alhouiti. Existence and uniqueness theorems for pointwise-slant immersions in Sasakian space forms[J]. AIMS Mathematics, 2023, 8(8): 17470-17483. doi: 10.3934/math.2023892

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Abstract

In this paper we derive the Existence and Uniqueness Theorems for pointwise slant immersions in Sasakian space forms which extend the Existence and Uniqueness Theorems for slant immersions in Sasakian space forms proved by Cabreizo et al in 2001.

References

[1]	A. Alghanemi, N. Al-Houiti, B. Chen, S. Uddin, Existence and uniqueness theorems for pointwise slant immersions in complex space forms, Filomat, 35 (2021), 3127–3138. http://dx.doi.org/10.2298/FIL2109127A doi: 10.2298/FIL2109127A
[2]	D. Blair, Contact manifolds in Riemannian geometry, Berlin: Springer-Verlag, 1976. http://dx.doi.org/10.1007/BFb0079307
[3]	J. Cabreizo, A. Carriazo, L. Fernandez, M. Fernandez, Existence and uniqueness theorem for slant immersions in Sasakian space forms, Publ. Math. Debrecen, 58 (2001), 559–574.
[4]	B. Chen, Geometry of submanifolds, New York: Dover Publication, 1973.
[5]	B. Chen, Slant immersions, Bull. Aust. Math. Soc., 41 (1990), 135–147. http://dx.doi.org/10.1017/S0004972700017925 doi: 10.1017/S0004972700017925
[6]	B. Chen, Geometry of slant submanifolds, arXiv: 1307.1512.
[7]	B. Chen, O. Garary, Pointwise slant submanifolds in almost Hermitian manifolds, Turk. J. Math., 36 (2012), 630–640. http://dx.doi.org/10.3906/mat-1101-34 doi: 10.3906/mat-1101-34
[8]	B. Chen, L. Vranken, Existence and uniqueness theorem for slant immersions and its applications, Results Math., 31 (1997), 28–39. http://dx.doi.org/10.1007/BF03322149 doi: 10.1007/BF03322149
[9]	B. Chen, L. Vranken, Addendum to: existence and uniqueness theorem for slant immersions and its applications, Results Math., 39 (2001), 18–22. http://dx.doi.org/10.1007/BF03322673 doi: 10.1007/BF03322673
[10]	J. Eschenburg, R. Tribuzy, Existence and uniqueness of maps into affine homogeneous spaces, Rend. Semin. Mat. Univ. Pad., 89 (1993), 11–18.
[11]	F. Etayo, On quasi-slant submanifolds of an almost Hermitian manifold, Publ. Math. Debrecen, 53 (1998), 217–223.
[12]	R. Gupta, S. Khursheed Haider, A. Sharfuddin, Existence and uniqueness theorem for slant immersion in cosymplectic space forms, Publ. Math. Debrecen, 67 (2005), 169–188.
[13]	S. Kumar, R. Prasad, Pointwise slant submersions from Sasakian manifolds, J. Math. Comput. Sci., 8 (2018), 454–466. http://dx.doi.org/10.28919/jmcs/3684 doi: 10.28919/jmcs/3684
[14]	A. Lotta, Slant submanifolds in contact geometry, Bull. Math. Soc. Roumanie, 39 (1996), 183–198.
[15]	P. Pandey, R. Gupta, Existence and uniqueness theorem for slant immersions in Kenmotsu space forms, Turk. J. Math., 33 (2009), 409–425. http://dx.doi.org/10.3906/mat-0804-23 doi: 10.3906/mat-0804-23
[16]	K. Park, Pointwise slant and Pointwise semi-slant submanifolds in almost contact metric manifolds, Mathematics, 8 (2020), 985. http://dx.doi.org/10.3390/math8060985 doi: 10.3390/math8060985
[17]	K. Park, Pointwise almost h-semi-slant submanifolds, Int. J. Math., 26 (2012), 15500998. http://dx.doi.org/10.1142/S0129167X15500998 doi: 10.1142/S0129167X15500998
[18]	B. Sahin, Warped product pointwise semi-slant submanifolds of Kähler manifolds, Port. Math., 70 (2013), 251–268. http://dx.doi.org/10.4171/PM/1934 doi: 10.4171/PM/1934
[19]	S. Tanno, Sasakian manifolds with constant $\phi$-holomorphic sectional curvature, Tohoku Math. J., 21 (1969), 501–507. http://dx.doi.org/10.2748/tmj/1178242960 doi: 10.2748/tmj/1178242960
[20]	S. Uddin, A. Al-Khalidi, Pointwise slant submanifolds and their Warped product in Sasakian manifolds, Filomat, 32 (2018), 4131–4142. http://dx.doi.org/10.2298/FIL1812131U doi: 10.2298/FIL1812131U

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