
Consider a Lagrangian immersion, i.e., an immersion of a Riemannian manifold \(M\) into a Kähler \(n\)-manifold \(\overline{M}\) such that it is an isometric immersion whose complex structure \(J\) of \(\overline{M}\) interchanges each tangent space of \(M\) with its corresponding normal space. A Lagrangian immersion is called Masolvian if its Maslov vector field \(JH\), where \(H\) is the mean curvature of \(M\), is a principal direction of the shape operator \(A_H\) of \(M\). The authors classify Maslovian Lagrangian immersions of real space forms of dimension \(\geq 3\) into complex space forms, completing the work of the first author, of \textit{N. Ejiri} [Proc. Am. Math. Soc. 84, 243--246 (1982; Zbl 0485.53022)] and several others. This paper is clearly written.
Differential geometry of immersions (minimal, prescribed curvature, tight, etc.), Local submanifolds, Lagrangian immersions, Global differential geometry of Hermitian and Kählerian manifolds, complex space form, Lagrangian cylinder, Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics, Maslovian Lagrangian immersion, Lagrangian submanifolds; Maslov index, Special Riemannian manifolds (Einstein, Sasakian, etc.), Maslovian immersions, Maslov form, Lagrangian immersion, Lagrangian pseudo-sphere, isometric immersions, real space form
Differential geometry of immersions (minimal, prescribed curvature, tight, etc.), Local submanifolds, Lagrangian immersions, Global differential geometry of Hermitian and Kählerian manifolds, complex space form, Lagrangian cylinder, Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics, Maslovian Lagrangian immersion, Lagrangian submanifolds; Maslov index, Special Riemannian manifolds (Einstein, Sasakian, etc.), Maslovian immersions, Maslov form, Lagrangian immersion, Lagrangian pseudo-sphere, isometric immersions, real space form
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