Abstract
<abstract><p>In this paper, we prove that an almost contact metric structure of a real hypersurface in a complex space form is quasi-contact if and only if it is contact. We also classify real hypersurfaces whose associated almost contact metric structures are nearly Kenmotsu or cosymplectic, which gives several extensions of some earlier results in this field.</p></abstract>
Publisher
American Institute of Mathematical Sciences (AIMS)
Reference33 articles.
1. T. Adachi, M. Kameda, S. Maeda, Geometric meaning of Sasakian space forms from the viewpoint of submanifold theory, Kodai Math. J., 33 (2010), 383–397. http://dx.doi.org/10.2996/kmj/1288962549
2. T. Adachi, M. Kameda, S. Maeda, Real hypersurfaces which are contact in a nonflat complex space form, Hokkaido Math. J., 40 (2011), 205–217. http://dx.doi.org/10.14492/hokmj/1310042828
3. J. Bae, J. Yeongjae, J. H. Park, K. Sekigawa, Quasi contact metric manifolds with Killing characteristic vector fields, B. Korean Math. Soc., 57 (2000), 1299–1306. http://dx.doi.org/10.4134/BKMS.b190981
4. D. E. Blair, Almost contact manifolds with Killing structure tensors, Pac. J. Math., 39 (1971), 285–292. http://dx.doi.org/10.2140/pjm.1971.39.285
5. D. E. Blair, Riemannian geometry of contact and symplectic manifolds, Progress in Mathematics, New York: Birkh$\ddot{\mathrm{a}}$user, 2010. http://dx.doi.org/10.1007/978-0-8176-4959-3