Title: δ-Invariants for Langrangian submanifolds of complex space forms
Authors: Chen, Bang-Yen *
Dillen, Franki * # ×
Issue Date: 2011
Publisher: editura universitãtii din bucuresti
Host Document: Riemannian Geometry and Applications pages:75-94
Conference: International Conference Riemannian Geometry and Applications location:Riga date:10-14 May 2011
Abstract: Abstract. The famous Nash embedding theorem published in 1956 was aiming for the opportunity to use extrinsic help in the study of(intrinsic) Riemannian geometry, if Riemannian manifolds could be regarded as Riemannian submanifolds. However, this hope had not been
materialized yet according to [23]. The main reason for this was the lack of control of the extrinsic properties of the submanifolds by the known intrinsic invariants. In order to overcome such difficulties as well as to provide answers to an open question on minimal immersions, the first author introduced in the early 1990’s new types of Riemannian invariants, his so-called -curvatures, different in nature from the “classical” Ricci and scalar curvatures.
One purpose of this article is to present some old and recent results concerning -invariants for Lagrangian submanifolds of complex space forms. Another purpose is to point out that the proof of Theorem 4.1 of [17] is not correct and the Theorem has to be reformulated. More
precisely, Theorem 4.1 of [17] shall be replaced by Theorems 8.1 and 8.3 of this article. Since the new formulation needs a new proof, we also provide the proofs of Theorems 8.1 and 8.3 in this article.
2000 Mathematics Subject Classification: Primary: 53C40; Secondary
53D12, 53C42
ISBN: 978-606-16-0053-3
Publication status: published
KU Leuven publication type: IC
Appears in Collections:Geometry Section
* (joint) first author
× corresponding author
# (joint) last author

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