PARALLEL ISOMETRIC IMMERSIONS AND KÄHLER FRENET CURVES

Hiromasa Tanabe (Japan)

Received August 31, 2005

References:

[1] J. Erbacher, Reduction of the codimension of an isotropic immersion, J. Differential Geom. 5 (1971), 333-340. [2] D. Ferus, Immersions with parallel second fundamental form, Math. Z. 140 (1974), 87-92. [3] S. Maeda and H. Tanabe, Totally geodesic immersions of Kähler manifolds and Kähler Frenet curves, Math. Z., to appear. [4] K. Nomizu and K. Yano, On circles and spheres in Riemannian geometry, Math. Ann. 210 (1974), 163-170. [5] B. O’Neill, Isotropic and Kähler immersions, Canad. J. Math. 17 (1965), 905-915. [6] K. Sakamoto, Planar geodesic immersions, Tôhoku Math. J. 29 (1977), 25-56. [7] M. Takeuchi, Parallel submanifolds of space forms, Manifolds and Lie Groups, in honor of Y. Matsushima, Birkhäuser, Boston, 1981, pp. 429-447. [8] H. Tanabe, Characterization of totally geodesic submanifolds in terms of Frenet curves, preprint.

Keywords and phrases: Kähler Frenet curves, parallel isometric immersions, complex space forms, real space forms.