Explore: Cr Submanifolds

intrinsically the property of being a hypersurface (or certain real submanifolds of higher codimension) in complex space by studying the properties of

ambient manifold. Submanifolds of space forms that satisfy the equality case of this inequality are known as ideal immersions; such submanifolds are critical

submanifolds, Marcel Dekker, New York 1976 Morio Obata (ed.): Selected papers of Kentaro Yano, North Holland 1982 with Masahiro Kon: CR Submanifolds of

The submanifolds are called the leaves of the foliation. The 3-sphere has a famous codimension-1 foliation called the Reeb foliation. The submanifolds are

Riemann surface Complex projective space Kähler manifold Dolbeault operator CR manifold Stein manifold Almost complex structure Hermitian manifold Newlander–Nirenberg

Eigenvalues of the Laplacian of compact Riemann surfaces and minimal submanifolds. Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 7 (1980), no. 1, 55–63. Chanillo

manifolds, namely immersions and submersions, and the intersections of submanifolds via transversality. More generally one is interested in properties and

is a generalization of the Laplace operator to functions defined on submanifolds in Euclidean space and, even more generally, on Riemannian and pseudo-Riemannian

a Lie group. Similarly, if the transition functions are: Cr then the vector bundle is a Cr vector bundle, real analytic then the vector bundle is a real

p-dimensional, class Cr foliation of an n-dimensional manifold M is a decomposition of M into a union of disjoint connected submanifolds {Lα}α∈A, called the