n-dimensional totally real minimal submanifolds of CP
n |
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Authors: | Domenico Perrone |
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Institution: | (1) Dipartimento di Matematica, Università degli Studi di Lecce, 73100 Lecce, Italy |
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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 τ, 0<τ ≦ 70/3, then M is locally isometric to S
1,5 :=S
1 (sin θ cos θ) × S
5 (sin θ), tan θ = √6.
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(b) |
If M is 4-dimensional, has parallel second fundamental form and scalar curvature τ ≧ 15/2, then M is locally isometric to S
1,3 :=S
1 (sin θ cos θ) × S
3 (sinθ), tan θ=2, or it is totally geodesic.
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Supported by funds of the M.U.R.S.T. |
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Keywords: | Mathematics Subject Classification (1991)" target="_blank">Mathematics Subject Classification (1991) 53C42 53C40 53C20 |
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