×

Characterizations of space forms by circles on their geodesic spheres. (English) Zbl 1030.53057

Starting from the previous work of the authors [Bull. Aust. Math. Soc. 62, No. 2, 205-210 (2000; Zbl 0978.53071)] where the space forms are characterized in terms of the extrinsic shape of geodesics in geodesic spheres, in this paper, the authors extend the obtained results by using circles on their geodesic spheres.
Reviewer: V.Cruceanu (Iaşi)

MSC:

53C40 Global submanifolds
53B25 Local submanifolds

Citations:

Zbl 0978.53071
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Adachi, T., and Maeda, S.: Space forms from the viewpoint of their geodesic spheres. Bull. Austral. Math. Soc., 62 , 205-210 (2000). · Zbl 0978.53071
[2] Adachi, T., Maeda, S., and Udagawa, S.: Circles in a complex projective space. Osaka J. Math., 32 , 709-719 (1995). · Zbl 0857.53034
[3] Chen, B.-Y., and Vanhecke, L.: Differential geometry of geodesic spheres. J. Reine Angew. Math., 325 , 28-67 (1981). · Zbl 0503.53013
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.