Abstract
In this paper the first and the second variation formulas for the area integral of the centroaffine metric of hypersurfaces in ℝn+1 are calculated, and some interesting examples of stable and unstable centroaffine minimal hypersurfaces are given.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Calabi, E.: Hypersurfaces with maximal affinely invariant area,Amer. J. Math. 140 (1982), 91–126.
Li, A. M.: Variational formulas for higher affine mean curvatures,Result. Math. 13 (1988), 318–326.
Dillen, F., Mys, G., Verstraelen, L. and Vrancken, L.: The affine mean curvature vector for surfaces in ℝ4 (Preprint, 1992).
Li, A. M. and Wang, C. P.: Canonical centroaffine hypersurfaces in ℝn+1,Result. Math. 20 (1991), 660–681.
Nomizu, K. and Sasaki, T.: Centroaffine immersions of codimension two and projective hyper-surface theory (MPI preprint 91-80, 1991).
Simon, U., Schwenk-Schellschmidt, A. and Viesel, H.:Introduction to the Affine Differential Geometry of Hypersurfaces, Lecture Notes, Science University of Tokyo, 1991.
Verstraelen, L. and Vrancken, L.: Affine variation formulas and affine minimal surfaces,Mich. Math. J. 36 (1) (1989), 77–93.
Voss, K.: Variation of curvature integrals,Result. Math. 20 (1991), 789–796.
Walter, R.: Centroaffine differential geometry, submanifolds of codimension 2,Result. Math. 13 (1988), 386–402.
Walter, R.: Compact centroaffine spheres of codimension 2,Result. Math. 20 (1991), 775–788.
Author information
Authors and Affiliations
Additional information
Partially supported by the DFG-project ‘Affine Differential Geometry’ at the TU Berlin.