Lagrangian submanifolds in complex space forms satisfying an improved equality involving δ(2,2)
It was proved in [8, 9] that every Lagrangian submanifold M of a complex space form M˜ 5 (4c) of constant holomorphic sectional curvature 4c satisfies the following optimal inequality: δ(2, 2) ≤ 25 4 H 2 + 8c, (A) where H 2 is the squared mean curvature and δ(2, 2) is a δ-invariant on M introduced b...
| Authors: | , , |
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| Format: | article |
| Status: | Published version |
| Publication Date: | 2013 |
| Country: | España |
| Institution: | Universidad de Sevilla (US) |
| Repository: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/42617 |
| Online Access: | http://hdl.handle.net/11441/42617 https://doi.org/10.5486/PMD.2013.5405 |
| Access Level: | Open access |
| Keyword: | Lagrangian submanifold improved inequality δ-invariants ideal submanifolds H-umbilical Lagrangian submanifold |
| Summary: | It was proved in [8, 9] that every Lagrangian submanifold M of a complex space form M˜ 5 (4c) of constant holomorphic sectional curvature 4c satisfies the following optimal inequality: δ(2, 2) ≤ 25 4 H 2 + 8c, (A) where H 2 is the squared mean curvature and δ(2, 2) is a δ-invariant on M introduced by the first author. This optimal inequality improves a special case of an earlier inequality obtained in [B.-Y. Chen, Japan. J. Math. 26 (2000), 105-127]. The main purpose of this paper is to classify Lagrangian submanifolds of M˜ 5 (4c) satisfying the equality case of the improved inequality (A). |
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