The measure of holomorphicness of a real submanifold of an almost Hermitian manifold

The geometry of a bi-Lagrangian manifold

“…This will be made by means of Plücker coordinates in the Grassmann manifold G(2, 4) of vector planes in R 4 . We use the notation of [20].…”

“…Then , ω Π = 0 iff ω(v, w) = 0, i.e., p 13 + p 24 = 0, which shows that the set of Lagrangian planes is a 3-dimensional manifold (because dim G(2, 4) = 4). Moreover, as is well known, Lagrangian planes are totally real planes when one considers the standard Kähler structure C 2 = R 4 (see [20,Proposition 12]).…”

“…(3)The theory of real submanifolds of complex manifolds shows a large collection of interesting submanifolds, such as complex, totally real, Cauchy-Riemann, slant, generic, etc. In a recent paper [20], one of the authors have obtained results about the holomorphicness of a real submanifold of an almost Hermitian manifold. It would be interesting to obtain similar results about submanifolds of a symplectic manifold, or, at least, about submanifolds of a bi-Lagrangian manifold.…”