On indefinite special Lagrangian submanifolds in indefinite complex Euclidean spaces

On Indefinite Special Lagrangian Submanifolds in Indefinite Complex Euclidean Spaces

In this paper, we show that the calibrated method can also be used to detect indefinite minimal Lagrangian submanifolds in C k . We introduce the notion of indefinite special Lagrangian submanifolds in C k and generalize the well-known work of Harvey-Lawson to the indefinite case.

Complex Extensors and Lagrangian Submanifolds in Complex Euclidean Spaces

Lagrangian //-umbilical submanifolds are the "simplest" Lagrangian submanifolds next to totally geodesic ones in complex-space-forms. The class of Lagrangian //-umbilical submanifolds in complex Euclidean spaces includes Whitney's spheres and Lagrangian pseudo-spheres. For each submanifold M of Euclidean «-space and each unit speed curve F in the complex plane, we introduce the notion of the co...

Classification of Spherical Lagrangian Submanifolds in Complex Euclidean Spaces

An isometric immersion f : Mn → M̃n from a Riemannian nmanifold Mn into a Kähler n-manifold M̃n is called Lagrangian if the complex structure J of the ambient manifold M̃n interchanges each tangent space of Mn with the corresponding normal space. In this paper, we completely classify spherical Lagrangian submanifolds in complex Euclidean spaces. In this paper, we also provide two corresponding cla...

Minimal Lagrangian Submanifolds in Complex Euclidean Space

Special Half Lightlike Submanifolds of an Indefinite Sasakian Manifold

In this paper, we study the geometry of half lightlike submanifolds of an indefinite Sasakian manifold. There are several different types of half lightlike submanifolds of an indefinite Sasakian manifold according to the form of its structure vector field. We study two types of them here: tangential and ascreen half lightlike submanifolds.