Examples of 'submanifolds' in a sentence
Meaning of "submanifolds"
submanifold (noun) - In mathematics and geometry, a submanifold is a subset of a manifold that is itself a manifold. Submanifolds are important in various mathematical theories, such as differential geometry and topology, and are used to study complex geometric shapes and structures. They provide a way to analyze and understand the properties of higher-dimensional spaces
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- plural of submanifold
How to use "submanifolds" in a sentence
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submanifolds
I am particularly interested in singularities of minimal submanifolds.
There are some other variations of submanifolds used in the literature.
Variance of the volume of random real algebraic submanifolds.
There are different types of submanifolds depending on exactly which properties are required.
The integral manifolds of these distributions are totally geodesic submanifolds.
It follows that immersed submanifolds are precisely the images of injective immersions.
The idea of an envelope of a family of smooth submanifolds follows naturally.
Lagrangian submanifolds arise naturally in many physical and geometric situations.
We give in this thesis some results of existence of such a submanifolds.
Geometric and topological properties of submanifolds and foliations of Riemannian.
We also approach the case of bernstein theorem for stable submanifolds.
We finally extend these results to submanifolds of some particular Kählerian manifolds.
We present in this thesis a few properties of monotone Lagrangian submanifolds.
The most important case of the isotropic submanifolds is that of Lagrangian submanifolds.
Let invariant submanifolds of a superintegrable Hamiltonian system be connected compact and mutually diffeomorphic.
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We also study the topology of a certain class of submanifolds of euclidean space.
That is, embedded submanifolds are precisely the images of embeddings.
Floer also developed a closely related theory for Lagrangian submanifolds of a symplectic manifold.
More generally, minimal submanifolds are harmonic immersions of one manifold in another.
We investigate the connection between the contact hamiltonian and these Legendre submanifolds.
The other strata are coisotropic or Legendrian submanifolds in the contact components that contain them.
In canonical gravity, spacetime is foliated into spacelike submanifolds.
Extrinsic geometric flows are flows on embedded submanifolds, or more generally immersed submanifolds.
If the maps are embeddings, this is equivalent to transversality of submanifolds.
In the rst part, we obtain classi cation theorems for submanifolds with positive biorthogonal curvature.
Inclusion maps in geometry come in different kinds, for example embeddings of submanifolds.
These are the same as Cr submanifolds with r 0.
He published results in integral geometry, value distribution theory of holomorphic functions, and minimal submanifolds.
Smooth manifolds are sometimes defined as embedded submanifolds of real coordinate space Rn, for some n.
Roughly speaking, they are what mathematicians call special Lagrangian submanifolds.
The simplest example of Legendrian submanifolds are Legendrian knots inside a contact three-manifold.
Generalisations = = The idea of an envelope of a family of smooth submanifolds follows naturally.
If the subspaces or submanifolds intersect transversally ( which occurs generically ), codimensions add exactly.
Namely, it is associated to a contact manifold and one of its Legendrian submanifolds.
Let X and Y be two disjoint locally closed submanifolds of Rn, of dimensions i and j.
In this thesis we investigate 3 and 4-dimensional minimal submanifolds.
Minimal and self-similar lagrangian submanifolds in the para-complex space.
In 1980 jorge and koutrofiotis proved optimal estimates of sectional curvature for extrinsically bounded submanifolds.
In the A-model, the D-branes can again be viewed as submanifolds of a Calabi-Yau manifold.
A Riemann surface is a 1-dimensional complex manifold, and so its codimension-1 submanifolds have dimension 0.
Other variations = = = There are some other variations of submanifolds used in the literature.
In this work, we study minimal and self-similar lagrangian submanifolds in the para-complex space $ d ^ n.
Abstract, The monotonicity condition for Lagrangian submanifolds was introduced by Oh in 1993.
