Abstract
Totally geodesic submanifolds of Riemannian symmetric spaces have been well investigated and it has been shown that they have beautiful and fruitful properties. In particular, due to the (M+,M_)-theory by B.Y. Chen and T. Nagano [1] this subject has made great progress. Naturally reductive homogeneous spaces are known as a natural generalization of Riemannian symmetric spaces. K. Tojo [6] investigated totally geodesic submanifolds of naturally reductive homogeneous spaces and obtained a necessary and sufficient condition of their existence. We will recall his result in section 3. Moreover he implicitly made the following conjecture.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
