Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Remote Access
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Constant isotropic submanifolds with $ 4$-planar geodesics


Authors: Jin Suk Pak and Kunio Sakamoto
Journal: Trans. Amer. Math. Soc. 307 (1988), 317-333
MSC: Primary 53C40
MathSciNet review: 936819
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let $ f$ be an isometric immersion of a Riemannian manifold $ M$ into $ \overline M $. We prove that if $ f$ is constant isotropic, $ 4$-planar geodesic and $ \overline M $ is a Euclidean sphere, then $ M$ is isometric to one of compact symmetric spaces of rank equal to one and $ f$ is congruent to a direct sum of standard minimal immersions. We also determine constant isotropic, $ 4$-planar geodesic, totally real immersions into a complex projective space of constant holomorphic sectional curvature.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 53C40

Retrieve articles in all journals with MSC: 53C40


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1988-0936819-7
PII: S 0002-9947(1988)0936819-7
Keywords: Second fundamental forms, isotropic and $ 4$-planar geodesic immersions, totally real immersions
Article copyright: © Copyright 1988 American Mathematical Society



Comments: Email Webmaster

© Copyright , American Mathematical Society
Contact Us · Sitemap · Privacy Statement

Connect with us Facebook Twitter Google+ LinkedIn Instagram RSS feeds Blogs YouTube Podcasts Wikipedia