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Báo cáo toán học: "Submanifolds with Parallel Mean Curvature Vector Fields and Equal Wirtinger Angles in Sasakian Space Forms"

Chúng tôi nghiên cứu đóng submanifolds M kích thước 2n + 1, đắm mình vào một (4N + 1) chiều Sasakian hình thức không gian (N, ξ, η, φ) với c cong φ-cắt liên tục, như vậy mà lĩnh vực vector Reeb ξ là tiếp tuyếnM. | 33 V í e t mi ai m J o u r mi ai l of MATHEMATICS ê VAST 2005 Submanifolds with Parallel Mean Curvature Vector Fields and Equal Wirtinger Angles in Sasakian Space Forms Guanghan Li School of Math. and Compt. Sci. Hubei University Wuhan 430062 China Abstract. . 1. Introduction and Main Theorem p This work was supported by National Natural Science Fund of China and Tianyuan Youth Fund in Mathematics. 2.2. Theorem 1.1. Let.be a.-dimensional Sasakian space form with constant -sectional curvature and a real.-dimensional closed submanifold tangent to with equal Wirtinger angles immersed into . If the mean curvature vector held of is parallel then When 3 is either an invariant or an anti--invariant submanifold. When 3 the common Wirtinger angles of must be constant. Remark 1.2. 2. Preliminaries and Formulas .2.