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ON SLANT RIEMANNIAN SUBMERSIONS FOR COSYMPLECTIC MANIFOLDS
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 Title & Authors
ON SLANT RIEMANNIAN SUBMERSIONS FOR COSYMPLECTIC MANIFOLDS
Erken, Irem Kupeli; Murathan, Cengizhan;
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 Abstract
In this paper, we introduce slant Riemannian submersions from cosymplectic manifolds onto Riemannian manifolds. We obtain some results on slant Riemannian submersions of a cosymplectic manifold. We also give examples and inequalities between the scalar curvature and squared mean curvature of fibres of such slant submersions in the cases where the characteristic vector field is vertical or horizontal.
 Keywords
Riemannian submersion;cosymplectic manifold;slant submersion;
 Language
English
 Cited by
1.
Conformal semi-invariant submersions, Communications in Contemporary Mathematics, 2017, 19, 02, 1650011  crossref(new windwow)
2.
Conformal semi-slant submersions, International Journal of Geometric Methods in Modern Physics, 2017, 14, 07, 1750114  crossref(new windwow)
3.
Semi-invariant submersions whose total manifolds are locally product Riemannian, Quaestiones Mathematicae, 2017, 1  crossref(new windwow)
4.
On anti-invariant Riemannian submersions whose total manifolds are locally product Riemannian, Journal of Geometry, 2017, 108, 2, 411  crossref(new windwow)
 References
1.
P. Baird and J. C. Wood, Harmonic Morphisms Between Riemannian Manifolds, London Mathematical Society Monographs, 29, Oxford University Press, The Clarendon Press, Oxford, 2003.

2.
D. E. Blair, Contact Manifolds in Riemannian Geometry, Lectures Notes in Mathematics 509, Springer-Verlag, Berlin, 1976.

3.
J. P. Bourguignon and H. B. Lawson, Stability and isolation phenomena for Yang-mills fields, Comm. Math. Phys. 79 (1981), no. 2, 189-230. crossref(new window)

4.
J. P. Bourguignon and H. B. Lawson, Mathematician's visit to Kaluza-Klein theory, Rend. Sem. Mat. Univ. Politec. Torino (1989), Special Issue, 143-163.

5.
J. L. Cabrerizo, A. Carriazo, L. M. Fernandez, and M. Fernandez, Slant submanifolds in Sasakian Manifolds, Glasg. Math. J. 42 (2000), no. 1, 125-138. crossref(new window)

6.
B. Y. Chen, Geometry of Slant Submanifolds, Katholieke Universiteit Leuven, Leuven, 1990.

7.
D. Chinea, Almost contact metric submersions, Rend. Circ. Mat. Palermo (2) 34 (1985), no. 1, 89-104. crossref(new window)

8.
R. H. Escobales Jr., Riemannian submersions with totally geodesic fibers, J. Differential Geom. 10 (1975), 253-276.

9.
A. Gray, Pseudo-Riemannian almost product manifolds and submersions, J. Math. Mech. 16 (1967), 715-737.

10.
S. Ianus, A. M. Ionescu, R. Mazzocco, and G. E. Vilcu, Riemannian submersions from almost contact metric manifolds, arXiv: 1102.1570v1 [math. DG]. crossref(new window)

11.
S. Ianus, R. Mazzocco, and G. E. Vilcu, Riemannian submersions from quaternionic manifolds, Acta Appl. Math. 104 (2008), no. 1, 83-89. crossref(new window)

12.
S. Ianus and M. Visinescu, Kaluza-Klein theory with scalar fields and generalized Hopf manifolds, Class. Quantum Gravity 4 (1987), 1317-1325. crossref(new window)

13.
S. Ianus and M. Visinescu, Space-time compactification and Riemannian submersions, In: Rassias, G.(ed.) The Mathematical Heritage of C. F. Gauss, (1991), 358-371, World Scientific, River Edge.

14.
B. H. Kim, Fibred Riemannian spaces with quasi Sasakian structure, Hiroshima Math. J. 20 (1990), no. 3, 477-513.

15.
I. Kupeli Erken and C. Murathan, Slant Riemannian submersions from Sasakian manifolds, arXiv: 1309.2487v1 [math. DG].

16.
G. D. Ludden, Submanifolds of cosymplectic manifolds, J. Differential Geom. 4 (1970), 237-244.

17.
C. Murathan and I. Kupeli Erken, Anti-invariant Riemannian submersions from cosymplectic manifolds, arXiv:1302.5108v1 [math. DG].

18.
M. T. Mustafa, Applications of harmonic morphisms to gravity, J. Math. Phys. 41 (2000), no. 10, 6918-6929. crossref(new window)

19.
Z. Olszak, On almost cosymplectic manifolds, Kodai Math. J. 4 (1981), no. 2, 239-250. crossref(new window)

20.
B. O'Neill, The fundamental equations of a submersion, Michigan Math. J. 13 (1966), 459-469. crossref(new window)

21.
B. O'Neill, Semi-Riemannian Geometry with Applications to Relativity, Academic Press, New York-London 1983.

22.
K. S. Park, H-slant submersions, Bull. Korean Math. Soc. 49 (2012), no. 2, 329-338. crossref(new window)

23.
K. S. Park, H-semi-invariant submersions, Taiwanese J. Math. 16 (2012), no. 5, 1865-1878.

24.
B. Sahin, Anti-invariant Riemannian submersions from almost Hermitian manifolds, Cent. Eur. J. Math. 8 (2010), no. 3, 437-447. crossref(new window)

25.
B. Sahin, Slant submersions from almost Hermitian manifolds, Bull. Math. Soc. Sci. Math. Roumanie (N.S) 54(102) (2011), no. 1, 93-105.

26.
B. Sahin, Riemannian submersions from almost Hermitian manifolds, Taiwanese J. Math. 17 (2013), no. 2, 629-659.

27.
B. Sahin, Semi-invariant submersions from almost Hermitian manifolds, Canad. Math. Bull. 56 (2013), no. 1, 173-183. crossref(new window)

28.
H. M. Tastan, On Lagrangian submersion, arXiv: 1311.1676v1 [math. DG].

29.
B. Watson, Almost Hermitian submersions, J. Differential Geom. 11 (1976), no. 1, 147-165.

30.
B. Watson, G, G'-Riemannian submersions and nonlinear gauge field equations of general relativity, In: Rassias, T. (ed.) Global Analysis-Analysis on manifolds, dedicated M. Morse, 324-349, Teubner-Texte Math., 57, Teubner, Leipzig, 1983.

31.
D. W. Yoon, Inequality for Ricci curvature of slant submanifolds in cosymplectic space forms, Turkish J. Math. 30 (2006), no. 1, 43-56.