ON THE INDEFINITE POSITIVE QUADRIC ℚ+n-2

Title & Authors
ON THE INDEFINITE POSITIVE QUADRIC ℚ+n-2
Hong, Seong-Kowan;

Abstract
The generalized Gaussian image of a spacelike surface in $\small{L^n}$ lies in the indefinite positive quadric $\small{{\mathbb{Q}}_+^{n-2}}$ in the open submanifold $\small{{\mathbb{C}}P_+^{n-1}}$ of the complex projective space $\small{{\mathbb{C}}P^{n-1}}$. The purpose of this paper is to find out detailed information about $\small{{\mathbb{Q}}_+^{n-2}{\subset}{\mathbb{C}}P_+^{n-1}}$.
Keywords
spacelike surface;the generalized Gauss map;indefinite quadric;
Language
English
Cited by
References
1.
Abe, K. and Magid, M., Indefinite Rigidity of Complex Submanifold and Maximal Surfaces, Mathematical Proceedings 106 (1989), no. 3, 481-494

2.
Akutagawa, K. and Nishigawa, S., The Gauss Map and Spacelike Surfaces with Prescribed Mean Curvature in Minkowski 3-Space, Tohoku Mathematical Journal 42 (1990), no. 1, 67-82.

3.
Asperti, Antonio C. and Vilhena, Jose Antonio M., Spacelike Surfaces in \$L^4\$ with Degenerate Gauss Map, Results in Mathematics 60 (2011), no. 1, 185-211.

4.
Graves, L., Codimension One Isometric Immersions between Lorentz Spaces, Ph.D. Thesis, Brown University, 1977.

5.
Kobayasi, O., Maximal Surfaces in the 3-dimensional Minkowski Space \$L^3\$, Tokyo J. Math. 6 (1983), 297-309.

6.
Milnor, T. K., Harmonic Maps and Classical Surface Theory in Minkowski 3-space, Trans. of AMS 280 (1983), 161-185.

7.
O'Neil, B., Semi-Riemannian Geometry, Academic Press, New York, 1983.

8.
Osserman, R.,A Survey of Minimal Surfaces, Dover, New York, 1986