[1] S. Lie, Geometrie der Beruhrungstransformationen. B.G. Teubner, Leipzig, (1896).
[2] H. Geiges, An Introduction to Contact Topology. Cambridge University Press, New York (2008).
[3] H. Geiges, A brief history of contact geometry and topology. Expo. Math. 19(1), 25-53 (2001).
[4] H. Geiges, Christiaan Huygens and contact geometry. Nieuw Arch. Wiskd (5). 6(2), 117-123. (2005).
[5] A. Bejancu, CR-submanifolds of a Kaehler manifold-I, Proc. Amer. Math. Soc., 69(1978), 135-42.
[6] M. H. Shahid, A. Sharfuddin and S.I. Husain, CR-submanifolds of a Sasakian manifold, Review Research Fac. Sc.,
Yogoslavia, 15(1985), 203-178.
[7] M. Kobayashi, CR-submanifolds of a Sasakian manifold, Tensor N. S., 35(1981), 297-307.
[8] K. Matsumoto, On contact CR-submanifolds of Sasakian manifolds, Inter J. Math. § Math. Sci, 16(1983), 313-326.
[9] G. D. Ludden, Submanifolds of cosymplectic manifold, J. Diff. Geometry, 4(1970), 237-244.
[10] A. Cabras, A. Ianus and Gh. Pitis, Extrinsic spheres and parallel submanifolds in cosymplectic manifolds Math, J. Toyama
Univ. 17(1994), 31-53.
[11] A. Bejancu and N. Papaghiuc, Semi-invariant submanifolds a Sasakian manifold, An. Sti. Univ. ’Al. I. Cuza’ Iasi Sect. Ia
Mat. 27(1981), 163-170.
[12] A. Bejancu and N. Papaghiuc, Semi-invariant submanifolds a Sasakian space form, Colloq. Math. 48(1984), 77-88.
[13] N. Papaghiuc, Almost semi-invariant submanifolds in Sasakian Space forms, An. s¸t. Univ. Ias¸ı. 29(1983), 5-10.
[14] N. Papaghiuc, Some theorems on semi-invariant submanifolds of a Sasakian manifold, An. Sti. Univ. ’Al. I. Cuza’ Ias¸ı Sect.
I a Mat. 32(1986), 73-76.
[15] C.L. Bejan,Almost semi-invariant submanifolds of a cosymplectic manifold, An. S¸ ti. Univ. ’Al. I. Cuza’ Iası Sect. I a Mat.
31(1985), 149-156.
[16] A. Cabras and P. Matzeu, Almost semi-invariant submanifolds of a cosymplectic manifold, Demonstratio Math. 19(1986),
no.2, 395-401.
[17] B. B. Sinha and R.N. Yadav, Semi-invariant submanifolds of a Kenmotsu manifold, Bull. cal. Math. Soc. 86, 405-412,
(1994).
[18] H. Öztürk, C. Murathan, N. Aktan, A.T. Vanli, Almost a-cosymplectic f -manifolds, Analele stııntıfıce ale unıversıtatıı
”AI.I Cuza” Dı ıas¸ı (S.N.) Matematica, Tomul LX, f.1. (2014).
[19] K. Yano, M. Kon, Structures on Manifolds, World Scientific, Singapore. (1984).
[20] K. I. Erken, P. Dacko and C. Murathan, Almost a-Paracosymplectic Manifolds, arXiv: 1402.6930v1.
[21] D.E. Blair, Geometry of Manifolds with structural group U(n)O(s), J.Differential Geometry, 4(1970), 155-167.
[22] A. Bejancu, Geometry of CR-Submanifolds, D.Reidel Publ. Co., Holland, 169p. (1986).
Semi-Invariant Submanifolds of Almost $\alpha$-Cosymplectic $f$-Manifolds
Year 2020,
Volume: 3 Issue: 1, 57 - 66, 25.03.2020
In this paper, we have and study several properties of semi-invariant submanifolds of an almost $\alpha$-cosymplectic $f$-manifold. We give an example and investigate the integrability conditions for the distributions involved in the definition of a semi-invariant submanifold of an almost $\alpha$-cosymplectic $f$-manifold.
[1] S. Lie, Geometrie der Beruhrungstransformationen. B.G. Teubner, Leipzig, (1896).
[2] H. Geiges, An Introduction to Contact Topology. Cambridge University Press, New York (2008).
[3] H. Geiges, A brief history of contact geometry and topology. Expo. Math. 19(1), 25-53 (2001).
[4] H. Geiges, Christiaan Huygens and contact geometry. Nieuw Arch. Wiskd (5). 6(2), 117-123. (2005).
[5] A. Bejancu, CR-submanifolds of a Kaehler manifold-I, Proc. Amer. Math. Soc., 69(1978), 135-42.
[6] M. H. Shahid, A. Sharfuddin and S.I. Husain, CR-submanifolds of a Sasakian manifold, Review Research Fac. Sc.,
Yogoslavia, 15(1985), 203-178.
[7] M. Kobayashi, CR-submanifolds of a Sasakian manifold, Tensor N. S., 35(1981), 297-307.
[8] K. Matsumoto, On contact CR-submanifolds of Sasakian manifolds, Inter J. Math. § Math. Sci, 16(1983), 313-326.
[9] G. D. Ludden, Submanifolds of cosymplectic manifold, J. Diff. Geometry, 4(1970), 237-244.
[10] A. Cabras, A. Ianus and Gh. Pitis, Extrinsic spheres and parallel submanifolds in cosymplectic manifolds Math, J. Toyama
Univ. 17(1994), 31-53.
[11] A. Bejancu and N. Papaghiuc, Semi-invariant submanifolds a Sasakian manifold, An. Sti. Univ. ’Al. I. Cuza’ Iasi Sect. Ia
Mat. 27(1981), 163-170.
[12] A. Bejancu and N. Papaghiuc, Semi-invariant submanifolds a Sasakian space form, Colloq. Math. 48(1984), 77-88.
[13] N. Papaghiuc, Almost semi-invariant submanifolds in Sasakian Space forms, An. s¸t. Univ. Ias¸ı. 29(1983), 5-10.
[14] N. Papaghiuc, Some theorems on semi-invariant submanifolds of a Sasakian manifold, An. Sti. Univ. ’Al. I. Cuza’ Ias¸ı Sect.
I a Mat. 32(1986), 73-76.
[15] C.L. Bejan,Almost semi-invariant submanifolds of a cosymplectic manifold, An. S¸ ti. Univ. ’Al. I. Cuza’ Iası Sect. I a Mat.
31(1985), 149-156.
[16] A. Cabras and P. Matzeu, Almost semi-invariant submanifolds of a cosymplectic manifold, Demonstratio Math. 19(1986),
no.2, 395-401.
[17] B. B. Sinha and R.N. Yadav, Semi-invariant submanifolds of a Kenmotsu manifold, Bull. cal. Math. Soc. 86, 405-412,
(1994).
[18] H. Öztürk, C. Murathan, N. Aktan, A.T. Vanli, Almost a-cosymplectic f -manifolds, Analele stııntıfıce ale unıversıtatıı
”AI.I Cuza” Dı ıas¸ı (S.N.) Matematica, Tomul LX, f.1. (2014).
[19] K. Yano, M. Kon, Structures on Manifolds, World Scientific, Singapore. (1984).
[20] K. I. Erken, P. Dacko and C. Murathan, Almost a-Paracosymplectic Manifolds, arXiv: 1402.6930v1.
[21] D.E. Blair, Geometry of Manifolds with structural group U(n)O(s), J.Differential Geometry, 4(1970), 155-167.
[22] A. Bejancu, Geometry of CR-Submanifolds, D.Reidel Publ. Co., Holland, 169p. (1986).
Beyendi, S., Aktan, N., & Sivridağ, A. İ. (2020). Semi-Invariant Submanifolds of Almost $\alpha$-Cosymplectic $f$-Manifolds. Communications in Advanced Mathematical Sciences, 3(1), 57-66.
AMA
Beyendi S, Aktan N, Sivridağ Aİ. Semi-Invariant Submanifolds of Almost $\alpha$-Cosymplectic $f$-Manifolds. Communications in Advanced Mathematical Sciences. March 2020;3(1):57-66.
Chicago
Beyendi, Selahattin, Nesip Aktan, and Ali İhsan Sivridağ. “Semi-Invariant Submanifolds of Almost $\alpha$-Cosymplectic $f$-Manifolds”. Communications in Advanced Mathematical Sciences 3, no. 1 (March 2020): 57-66.
EndNote
Beyendi S, Aktan N, Sivridağ Aİ (March 1, 2020) Semi-Invariant Submanifolds of Almost $\alpha$-Cosymplectic $f$-Manifolds. Communications in Advanced Mathematical Sciences 3 1 57–66.
IEEE
S. Beyendi, N. Aktan, and A. İ. Sivridağ, “Semi-Invariant Submanifolds of Almost $\alpha$-Cosymplectic $f$-Manifolds”, Communications in Advanced Mathematical Sciences, vol. 3, no. 1, pp. 57–66, 2020.
ISNAD
Beyendi, Selahattin et al. “Semi-Invariant Submanifolds of Almost $\alpha$-Cosymplectic $f$-Manifolds”. Communications in Advanced Mathematical Sciences 3/1 (March 2020), 57-66.
JAMA
Beyendi S, Aktan N, Sivridağ Aİ. Semi-Invariant Submanifolds of Almost $\alpha$-Cosymplectic $f$-Manifolds. Communications in Advanced Mathematical Sciences. 2020;3:57–66.
MLA
Beyendi, Selahattin et al. “Semi-Invariant Submanifolds of Almost $\alpha$-Cosymplectic $f$-Manifolds”. Communications in Advanced Mathematical Sciences, vol. 3, no. 1, 2020, pp. 57-66.
Vancouver
Beyendi S, Aktan N, Sivridağ Aİ. Semi-Invariant Submanifolds of Almost $\alpha$-Cosymplectic $f$-Manifolds. Communications in Advanced Mathematical Sciences. 2020;3(1):57-66.