A totally real surface in $CP^{2}$ that is not totally geodesic
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- by Gerald D. Ludden, Masafumi Okumura and Kentaro Yano PDF
- Proc. Amer. Math. Soc. 53 (1975), 186-190 Request permission
Abstract:
An example of a totally real surface immersed in complex projective space is given. This surface is not totally geodesic. The relation of this example to previous theorems on totally real submanifolds is given.References
- Kinetsu Abe, Applications of a Riccati type differential equation to Riemannian manifolds with totally geodesic distributions, Tohoku Math. J. (2) 25 (1973), 425–444. MR 350671, DOI 10.2748/tmj/1178241276
- Bang-yen Chen and Koichi Ogiue, On totally real submanifolds, Trans. Amer. Math. Soc. 193 (1974), 257–266. MR 346708, DOI 10.1090/S0002-9947-1974-0346708-7
- S. S. Chern, M. do Carmo, and S. Kobayashi, Minimal submanifolds of a sphere with second fundamental form of constant length, Functional Analysis and Related Fields (Proc. Conf. for M. Stone, Univ. Chicago, Chicago, Ill., 1968) Springer, New York, 1970, pp. 59–75. MR 0273546
- Chorng-shi Houh, Some totally real minimal surfaces in $CP^{2}$, Proc. Amer. Math. Soc. 40 (1973), 240–244. MR 317189, DOI 10.1090/S0002-9939-1973-0317189-9
- H. Blaine Lawson Jr., Rigidity theorems in rank-$1$ symmetric spaces, J. Differential Geometry 4 (1970), 349–357. MR 267492 G. D. Ludden, M. Okumura and K. Yano, Real submanifolds of complex manifolds, Rend. Accad. Naz. Lincei (to appear). M. Okumura, Submanifolds of real codimension $p$ of a complex projective space (to appear).
- Barrett O’Neill, The fundamental equations of a submersion, Michigan Math. J. 13 (1966), 459–469. MR 200865
Additional Information
- © Copyright 1975 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 53 (1975), 186-190
- MSC: Primary 53C40
- DOI: https://doi.org/10.1090/S0002-9939-1975-0380683-0
- MathSciNet review: 0380683