Applications of Bochner formula to minimal submanifold of the sphere

✍ Scribed by A. Barros

• Publisher: Elsevier Science
• Year: 2002
• Tongue: English
• Weight: 61 KB
• Volume: 44
• Category: Article
• ISSN: 0393-0440
• DOI: 10.1016/s0393-0440(02)00061-x

✦ Synopsis

The aim of this note is to study some properties of compact minimal submanifolds M n of the Euclidean sphere S N . We will give estimates for the first eigenvalue of the Laplacian of M n as well as present a new estimate for the norm of the second fundamental form for hypersurfaces. Moreover, we obtain a new characterization of the sphere S n .