The aim of the present paper is to find necessary and sufficient conditions for locally ϕ-symmetric generalized Sasakian-space forms to have constant scalar curvature, η -parallel Ricci tensor, and cyclic parallel Ricci tensor. Illustrative examples are given.
References
P. Alegre, D. Blair, and A. Carriazo, “Generalized Sasakian-space forms,” Isr. J. Math., 14, 157–183 (2004).
P. Alegre and A. Carriazo, “Structures on generalized Sasakian-space forms,” Different. Geom. Appl., 26, 656–666 (2008).
D. E. Blair, Lecture Notes in Mathematics, Springer, Berlin, 509 (1976).
U. C. De and A. Sarkar, “Some results on generalized Sasakian-space forms,” Thai. J. Math., 8, 1–10 (2010).
U. C. De and A. Sarkar, “On three-dimensional trans-Sasakian manifolds,” Extracta Math., 23, 265–277 (2008).
U. C. De and A. Sarkar, “On three-dimensional quasi-Sasakian manifolds,” SUT J. Math., 45, 59–71 (2009).
S. Golab, “On semisymmetric and quarter-symmetric linear connections,” Tensor (New. Ser.), 29, 249–254 (1975).
A. Gray, “Two classes of Riemannian manifolds,” Geom. Dedic., 7, 259–280 (1978).
U. K. Kim, “Conformally flat generalized Sasakian-space forms and locally symmetric generalized Sasakian-space forms,” Note Mat., 26, 55–67 (2006).
U.-H. Ki and H. A. Nakagawa, “A characterization of Cartan hypersurfaces in a sphere,” Tohoku Math. J., 39, 27–40 (1987).
M. Kon, “Invariant submanifolds in Sasakian manifolds,” Math. Ann., 219, 277–290 (1976).
Z. Olszak, “On the existence of generalized complex space forms,” Isr. J. Math., 65, 214–218 (1989).
T. Takahashi, “Sasakian ϕ-symmetric spaces,” Tohoku Math. J., 29, 91–113 (1977).
K. Yano and S. Swaki, “Riemannian manifolds admitting a conformal transformation group,” J. Different. Geom., 2, 161–184 (1968).
K. Yano, “Integral formulas in Riemannian geometry,” Pure Appl. Math., No. 1 (1970).
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Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 65, No. 10, pp. 1430–1438, October, 2013.
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Sarkar, A., Sen, M. Locally ϕ-Symmetric Generalized Sasakian-Space Forms. Ukr Math J 65, 1588–1597 (2014). https://doi.org/10.1007/s11253-014-0881-3
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DOI: https://doi.org/10.1007/s11253-014-0881-3