In the present paper submanifolds of generalized Sasakian-spaceforms are studied. We focus on almost semi-invariant submanifolds, these generalize invariant, anti-invariant, and slant submanifolds. Sectional curvatures, Ricci tensor and scalar curvature are also studied. The paper finishes with some results about totally umbilical submanifolds.
References
P. Alegre, D. E. Blair and A. Carriazo, Generalized Sasakian space forms, Israel J. Math., 141 (2004), 157-183. MR2063031 1064.53026 10.1007/BF02772217 P. Alegre, D. E. Blair and A. Carriazo, Generalized Sasakian space forms, Israel J. Math., 141 (2004), 157-183. MR2063031 1064.53026 10.1007/BF02772217
P. Alegre and A. Carriazo, Structures on generalized Sasakian-space-forms, Differential Geom Appl., 26 (2008), 656-666. 1156.53027 10.1016/j.difgeo.2008.04.014 P. Alegre and A. Carriazo, Structures on generalized Sasakian-space-forms, Differential Geom Appl., 26 (2008), 656-666. 1156.53027 10.1016/j.difgeo.2008.04.014
M. Barros and F. Urbano, CR-submanifolds of generalized complex space forms. An. Stiint. Univ. Al. I. Cuza Iasi., 25 (1979), 355-363. MR562323 0418.53022 M. Barros and F. Urbano, CR-submanifolds of generalized complex space forms. An. Stiint. Univ. Al. I. Cuza Iasi., 25 (1979), 355-363. MR562323 0418.53022
A. Bejancu, CR-submanifolds of a Kaehler manifold. I, Proc. Amer. Math. Soc., 69(1) (1978), 135-142. MR467630 0368.53040A. Bejancu, CR-submanifolds of a Kaehler manifold. I, Proc. Amer. Math. Soc., 69(1) (1978), 135-142. MR467630 0368.53040
A. Bejancu and N. Papaghiuc, Almost semi-invariant submanifolds of a Sasakian manifold, Bull. Math. Soc. Sci. Math. R. S. Roumanie., 28 (1984), 13-40. MR744745 0535.53042 A. Bejancu and N. Papaghiuc, Almost semi-invariant submanifolds of a Sasakian manifold, Bull. Math. Soc. Sci. Math. R. S. Roumanie., 28 (1984), 13-40. MR744745 0535.53042
D. E. Blair, Riemannian Geometry of Contact and Symplectic Manifolds, Birkhäuser, Boston, 2002. 1011.53001 D. E. Blair, Riemannian Geometry of Contact and Symplectic Manifolds, Birkhäuser, Boston, 2002. 1011.53001
D. E. Blair and Lieven Vanhecke, Umbilical submanifolds of Sasakian space forms, J. Differential Geometry, 13(2) (1978), 273-278. 0435.53018 10.4310/jdg/1214434489D. E. Blair and Lieven Vanhecke, Umbilical submanifolds of Sasakian space forms, J. Differential Geometry, 13(2) (1978), 273-278. 0435.53018 10.4310/jdg/1214434489
B.-Y. Chen, Slant immersions, Bull. Austral. Math. Soc., 41 (1990), 135-147. 0677.53060 10.1017/S0004972700017925 B.-Y. Chen, Slant immersions, Bull. Austral. Math. Soc., 41 (1990), 135-147. 0677.53060 10.1017/S0004972700017925
B.-Y. Chen and K. Ogiue, Two theorems on Kaehler manifolds, Michigan Math. J., 21 (1975), 225-229. MR367884 euclid.mmj/1029001308
B.-Y. Chen and K. Ogiue, Two theorems on Kaehler manifolds, Michigan Math. J., 21 (1975), 225-229. MR367884 euclid.mmj/1029001308
F. Etayo, On Quasi-slant submanifolds of an almost Hermitian manifold, Publ. Math. Debrecen, 53(1-2) (1998), 217-223. 0981.53038 F. Etayo, On Quasi-slant submanifolds of an almost Hermitian manifold, Publ. Math. Debrecen, 53(1-2) (1998), 217-223. 0981.53038
G. S. Ronsse, Generic and skew CR submanifolds of a Kaehler manifold, Bull. Inst. Math. Acad. Sinica, 18 (1990), 127-141. MR1071229 0703.53018 G. S. Ronsse, Generic and skew CR submanifolds of a Kaehler manifold, Bull. Inst. Math. Acad. Sinica, 18 (1990), 127-141. MR1071229 0703.53018
M. M. Tripathi, Almost semi-invariant submanifolds of trans-Sasakian mani-folds, J. Indian Math. Soc., 62 (1996), 225-245. 0901.53040 M. M. Tripathi, Almost semi-invariant submanifolds of trans-Sasakian mani-folds, J. Indian Math. Soc., 62 (1996), 225-245. 0901.53040
M. M. Tripathi, Generic submanifolds of generalized complex space form, Publ. Math. Debrecen, 50 (1997), 373-392. MR1446480 0881.53043 M. M. Tripathi, Generic submanifolds of generalized complex space form, Publ. Math. Debrecen, 50 (1997), 373-392. MR1446480 0881.53043
M. M. Tripathi and Ion Mihai, Submanifolds of Framed Metric manifolds and S-manifolds, Note Mat., 20(2) (2001), 135-164. 1097.53037 M. M. Tripathi and Ion Mihai, Submanifolds of Framed Metric manifolds and S-manifolds, Note Mat., 20(2) (2001), 135-164. 1097.53037
M. M. Tripathi and K. D. Singh, Almost semi-invariant submanifolds of an $\xi$-framed metric manifold, Demonstratio Math., 29 (1996), 413-426. MR1407853 0896.53041 M. M. Tripathi and K. D. Singh, Almost semi-invariant submanifolds of an $\xi$-framed metric manifold, Demonstratio Math., 29 (1996), 413-426. MR1407853 0896.53041
L. Vanhecke, Umbilical Submanifolds of Generalized Complex Space Forms, Bull. Inst. Math. Acad. Sinica, 4 (1976), 183-190. MR458330 0348.53012 L. Vanhecke, Umbilical Submanifolds of Generalized Complex Space Forms, Bull. Inst. Math. Acad. Sinica, 4 (1976), 183-190. MR458330 0348.53012
