Sushil Kumar, Sumeet Kumar, Shashikant Pandey

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Riemannian maps are generalization of well-known notions of isometric immersions and Riemannian submersions. In this paper, we defne and study a natural generalization of previously defned quasi bi-slant submersions [18] in the case of Riemannian maps. We mainly investigate fundamental results on quasi bi-slant Riemannian maps from almost Hermitian manifolds to Riemannian manifolds: the integrability of distributions, geometry of foliations, the condition for such maps to be totally geodesic, etc. At the end of the article, we give proper non-trivial examples for this notion.


Riemannian maps, Quasi bi-slant Riemannian maps, Almost Hermitian manifolds

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bibitem{sk7} A.E. Fischer, textit{Riemannian maps between Riemannian

manifolds}, Contemporary Math. textbf{132} (1992), 331-366.

bibitem{skg} A. Gray, textit{Pseudo-Riemannian almost product manifolds

and submersions}, J. Math. Mech., textbf{16} (1967), 715-737.

bibitem{sk16} B. Sahin, textit{Riemannian submersions, Riemannian maps in

Hermitian geometry, and their applications}, Elsevier, Academic

Press (2017).

bibitem{sk17} B. Sahin, textit{Invariant and anti-invariant Riemannian

maps to Kahler manifolds}, Int. J. Geom. Methods Mod. Phys., textbf{7} (2010), no. 3, 337-355.

bibitem{sk18} B. Sahin, textit{Semi-invariant Riemannian maps from almost

Hermitian manifolds}, Indagationes Math., textbf{23} (2012),


bibitem{sk19} B. Sahin, textit{Slant Riemannian maps from almost Hermitian

manifolds}, Quaest. Math., textbf{36} (2013), n. 3, 449-461.

bibitem{sk20} B. Sahin, textit{Hemi-slant Riemannian Maps}, Mediterr. J. Math., textbf{14} (2017), no. 1, 1-17.

bibitem{osk} B. O'Neill, textit{The fundamental equations of a submersions}, Mich. Math. J., textbf{13} (1966), no. 4, 458-469.

bibitem{sk21} B. Watson, textit{Almost Hermitian submersions}, J.

Differential Geom., textbf{11} (1976), no. 1, 147-165.

bibitem{sk2} J. P. Bourguignon and H.B. Lawson, textit{Stability and

isolation phenomena for Yang-mills fields}, Commun. Math. Phys.,

textbf{79} (1981), 189-230.

bibitem{sk3} J. P. Bourguignon and H. B. Lawson, textit{A mathematician's

visit to Kaluza Klein theory}, Rend. Semin. Mat. Univ. Politec.

Torino Special Issue., (1989), 143-163.

bibitem{sk9} K. S. Park, and B. Sahin textit{Semi-slant

Riemannian maps into almost Hermitian manifolds}, Czech. Math. J., textbf{64} (2014), no. 4, 1045 -1061.

bibitem{sk1} P. Baird and J.C. Wood, textit{Harmonic Morphism between

Riemannian Manifolds}, Oxford science publications, Oxford (2003).

bibitem{sk4} P. Chandelas, G.T. Horowitz, A. Strominger and E. Witten,

textit{Vacuum configurations for super-strings}, Nuclear Physics B, textbf{

} (1985), 46-74.

bibitem{sk10} R. Prasad and S. Pandey, textit{Slant Riemannian maps from

an almost contact manifold}, Filomat, textbf{31} (2017), no. 13,


bibitem{RS1} R. Prasad and S. Pandey, textit{Semi-slant Riemannian maps from almost contact manifolds}

Analele Universitatii, Oradea Fasc. Matematica, Tom XXV (2018),

Issue No. 2, 127141.

bibitem{RS2} R. Prasad and S. Pandey, textit{Hemi-slant Riemannian maps from almost contact metric manifolds}, PJM, textbf{9} (2020), no. 2,


bibitem{sk11} R. Prasad, S.S. Shukla and S. Kumar, On Quasi bi-slant

Submersions, Mediterr. J. Math., textbf{16} (2019), 16:155,

bibitem{sk12} R. Prasad and S. Kumar, textit{Slant Riemannian maps from

Kenmotsu manifolds into Riemannian manifolds}, Global J. Pure Appl. Math., textbf{13} (2017), no. 4, 1143-1155.

bibitem{sk13} R. Prasad and S. Kumar, textit{Semi-slant Riemannian maps

from almost contact metric manifolds into Riemannian manifolds},

Tbilisi Mathematical Journal, textbf{11} (2018), no. 4, 19 -34.

bibitem{sk14} R. Prasad, S. Kumar, S. Kumar and A. T. Vanli, textit{On

Quasi-Hemi-Slant Riemannian Maps}, Gazi University Journal of

Science, textbf{34} (2021), no. 2, 477-491.

bibitem{sk15} R. Prasad and S. Kumar, textit{Semi-slant Riemannian maps

from Cosymplectic manifolds into Riemannian manifolds}, Gulf Journal

of Mathematics., textbf{9} (2020), no. 1, 62-80.

bibitem{sk8} T. Nore, textit{Second fundamental form of a map}, Ann Mat

Pur Appl., textbf{146} (1987), 281-310.

bibitem{sk6} U.C. De and A.A. Shaikh, textit{Differential Geometry of

Manifolds}, Narosa Pub. House (2009).

bibitem{sk5} V. Cortes, C Mayer, T. Mohaupt and F. Saueressig, textit{%

Special geometry of Euclidean super-symmetry}, Vector multiplets, J.

High Energy Phys., textbf{03} (2004), 028.



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