Geodesic
Ricci and scalar curvatures of submanifolds of a conformal Sasakian space form
Archivum mathematicum, Tome 52 (2016) no. 2, pp. 113-130 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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We introduce a conformal Sasakian manifold and we find the inequality involving Ricci curvature and the squared mean curvature for semi-invariant, almost semi-invariant, $\theta $-slant, invariant and anti-invariant submanifolds tangent to the Reeb vector field and the equality cases are also discussed. Also the inequality involving scalar curvature and the squared mean curvature of some submanifolds of a conformal Sasakian space form are obtained.
We introduce a conformal Sasakian manifold and we find the inequality involving Ricci curvature and the squared mean curvature for semi-invariant, almost semi-invariant, $\theta $-slant, invariant and anti-invariant submanifolds tangent to the Reeb vector field and the equality cases are also discussed. Also the inequality involving scalar curvature and the squared mean curvature of some submanifolds of a conformal Sasakian space form are obtained.
DOI : 10.5817/AM2016-2-113
Classification : 53C25, 53C40, 53D15
Keywords: Ricci curvature; scalar curvature; squared mean curvature; conformal Sasakian space form 
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Abedi, Esmaeil; Ziabari, Reyhane Bahrami; Tripathi, Mukut Mani. Ricci and scalar curvatures of submanifolds of a conformal Sasakian space form. Archivum mathematicum, Tome 52 (2016) no. 2, pp. 113-130. doi: 10.5817/AM2016-2-113

[1] Bejancu, A.: Geometry of CR-submanifolds. Mathematics and its Applications (East European Series), vol. 23, D. Reidel Publishing Co., Dordrecht, 1986. | MR | Zbl

[2] Blair, D.E.: Contact manifolds in Riemannian geometry. Math., vol. 509, Springer-Verlag, New York, 1976. | MR | Zbl

[3] Blair, D.E.: Riemannian geometry of contact and symplectic manifolds. Progress in Mathematics, vol. 203, Birkhauser Boston, Inc., Boston, MA, 2002. | MR | Zbl

[4] Cabrerizo, J.L., Carriazo, A., Fernandez, L.M., Fernandez, M.: Slant submanifolds in Sasakian manifolds. Glasgow Math. J. 42 (1) (2000), 125–138. | DOI | MR | Zbl

[5] Chen, B.Y.: Some pinching and classification theorems for minimal submanifolds. Arch. Math. (Basel) 60 (6) (1993), 568–578. | DOI | MR | Zbl

[6] Chen, B.Y.: Mean curvature and shape operator of isometric immersions in real space form. Glasgow Math. J. 38 (1996), 87–97. | DOI | MR

[7] Chen, B.Y.: Relations between Ricci curvature and shape operator for submanifolds with arbitrary codimensions. Glasgow Math. J. 41 (1999), 33–41. | DOI | MR | Zbl

[8] Chen, B.Y.: On Ricci curvature of isotropic and Lagrangian submanifolds in complex space forms. Arch. Math. (Basel) 74 (2000), 154–160. | DOI | MR | Zbl

[9] Defever, F., Mihai, I., Verstrelen, L.: B.Y.Chen’s inequality for $C$-totally real submanifolds of Sasakian space forms. Boll. Un. Mat. Ital. B (7) 11 (1997), 365–374. | MR

[10] Hong, S., Tripathi, M.M.: On Ricci curvature of submanifolds. Internat. J. Pure Appl. Math. Sci. 2 (2) (2005), 227–245. | MR | Zbl

[11] Hong, S., Tripathi, M.M.: On Ricci curvature of submanifolds of generalized Sasakian space forms. Internat. J. Pure Appl. Math. Sci. 2 (2) (2005), 173–201. | MR | Zbl

[12] Hong, S., Tripathi, M.M.: Ricci curvature of submanifolds of a Sasakian space form. Iranian Journal of Mathematical Sciences and Informatics 1 (2) (2006), 31–51. | MR | Zbl

[13] Mihai, I.: Ricci curvature of submanifolds in Sasakian space forms. J. Austral. Math. Soc. 72 (2002), 247–256. | DOI | MR | Zbl

[14] Petersen, P.: Riemannian geometry. Springer-Verlag, 2006. | MR | Zbl

[15] Tripathi, M.M.: Almost semi-invariant submanifolds of trans-Sasakian manifolds. J. Indian Math. Soc. (N.S.) 62 (1–4) (1996), 225–245. | MR | Zbl

[16] Vaisman, I.: Conformal changes of almost contact metric structures. Geometry and Differential Geometry, Lecture Notes in Math., vol. 792, 1980, pp. 435–443. | MR | Zbl

[17] Yamaguchi, S., Kon, M., Ikawa, T.: C-totallly real submanifolds. J. Differential Geom. 11 (1) (1976), 59–64. | DOI | MR

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