ISSN:
1420-8938
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract. Let CP n be the n-dimensional complex projective space with the Study-Fubini metric of constant holomorphic sectional curvature 4 and let M be a compact, orientable, n-dimensional totally real minimal submanifold of CP n . In this paper we prove the following results.¶(a) If M is 6-dimensional, conformally flat and has non negative Euler number and constant scalar curvature $ \tau, 0 〈 \tau \leq 70/3 $ , then M is locally isometric to $ S_{1,5} := S\,^{1}(\hbox {sin}\,\theta \,\hbox {cos}\,\theta )\times S\,^{5}(\hbox {sin}\,\theta ), \ \hbox {tan}\,\theta =\sqrt 6 $ .¶(b) If M is 4-dimensional, has parallel second fundamental form and scalar curvature $ \tau \geq {15}/2, $ then M is locally isometric to $ S_{1,3} := S\,^{1}(\hbox {sin}\,\theta \,\hbox {cos}\,\theta )\times S\,^{3}(\hbox {sin}\theta ), \hbox {tan}\,\theta =2 $ , or it is totally geodesic.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/s000130050066
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