6 edition of **Infinite Dimensional Kähler Manifolds (Oberwolfach Seminars)** found in the catalog.

- 234 Want to read
- 37 Currently reading

Published
**September 21, 2001**
by Birkhäuser Basel
.

Written in English

- Differential & Riemannian geometry,
- Topology,
- Mathematics,
- Differential Geometry,
- Science/Mathematics,
- Geometry - Differential,
- Geometry,
- Mathematics / General,
- complex analysis,
- group theory

**Edition Notes**

Contributions | Alan Huckleberry (Editor), Tilmann Wurzbacher (Editor) |

The Physical Object | |
---|---|

Format | Paperback |

Number of Pages | 375 |

ID Numbers | |

Open Library | OL9521739M |

ISBN 10 | 3764366028 |

ISBN 10 | 9783764366025 |

String theory says we live in a ten-dimensional universe, but that only four are accessible to our everyday senses. According to theorists, the missing six are curled up in bizarre structures known as Calabi-Yau manifolds. In The Shape of Inner Space, Shing-Tung Yau, the man who mathematically proved that these manifolds exist, argues that not only is geometry 5/5(2). Complex Monge–Ampère Equations and Geodesics in the Space of Kähler Metrics (Lecture Notes in Mathematics Book ) - Kindle edition by Guedj, Vincent. Download it once and read it on your Kindle device, PC, phones or tablets. Use features like bookmarks, note taking and highlighting while reading Complex Monge–Ampère Equations and Geodesics in the Space of Kähler Price: $

In mathematics and especially differential geometry, a Kähler manifold is a manifold with three mutually compatible structures; a complex structure, a Riemannian structure, and a symplectic a Kähler manifold X there exists Kähler potential and the Levi-Civita connection corresponding to the metric of X gives rise to a connection on the canonical line bundle. aims were cohomology of Kahler manifolds, formality of Kahler manifolds af-ter [DGMS], Calabi conjecture and some of its consequences, Gromov’s Kahler hyperbolicity [Gr], and the Kodaira embedding theorem. Let Mbe a complex manifold. A Riemannian metric on Mis called Her-mitian if it is compatible with the complex structure Jof M, hJX,JYi= hX,Yi.

This text on analysis of Riemannian manifolds is a thorough introduction to topics covered in advanced research monographs on Atiyah-Singer index theory. The main theme is the study of heat flow associated to the Laplacians on differential by: A somewhat more mathematical answer is Vinogradov's diffiety theory. There are many new things which have sprung up around the theory, but they center around diffieties: infinite-dimensional manifolds which represent the "space of all solutions" to a PDE, in a manner analogous to varieties in algebraic geometry.

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Infinite dimensional manifolds, Lie groups and algebras arise naturally in many areas of mathematics and physics. Having been used mainly as a tool for the study of finite dimensional objects, the emphasis has changed and they are now frequently studied for their own independent interest.

Infinite dimensional manifolds, Lie groups and algebras arise naturally in many areas of mathematics and physics. Rating: (not yet rated) 0 with reviews - Be the first. Get this from a library. Infinite Dimensional Kähler Manifolds. [Alan Huckleberry; Tilmann Wurzbacher] -- Infinite dimensional manifolds, Lie groups and algebras arise naturally in many areas of mathematics and physics.

Having been used mainly as a tool for the study of finite dimensional objects, the. This book describes Calabi's original work on Kähler immersions of Kähler manifolds into complex space forms, it provides a detailed account of what is known today on the subject and points out open problems.

The prerequisites are a basic knowledge of complex and Kähler geometry. In this book we study three important classes of infinite-dimensional Kähler manifolds — loop spaces of compact Lie groups, Teichmüller spaces of complex structures on loop spaces, and Grassmannians of Hilbert spaces.

Robert Geroch's lecture notes "Infinite-Dimensional Manifolds" provide a concise, clear, and helpful introduction to a wide range of subjects, which are essential in mathematical and theoretical physics - Banach spaces, open mapping theorem, splitting, bounded linear mappings, derivatives, mean value theorem, manifolds, mappings of manifolds, scalar and vector fields, 5/5(1).

Abstract: The study of Kähler immersions of a given real analytic Kähler manifold into a finite or infinite dimensional complex space form originates from the pioneering work of Eugenio Calabi [10].

With a stroke of genius Calabi defines a powerful tool, a special (local) potential called diastasis function, which allows him to obtain necessary and sufficient Cited by: $\begingroup$ For infinite dimensional smooth and Riemannian manifolds, Serge Lang's books are popular as a start.

$\endgroup$ – Claudio Gorodski Mar 30 '14 at 4 $\begingroup$ Why don't you list (in the question) the books you've already "seen", then. $\endgroup$ – Francois Ziegler Mar 30 '14 at Hilbert flag varieties and their Kähler structure. (Memorandum Faculty Mathematical Sciences; No.

Enschede: University of Twente, Department of Applied Mathematics. Book/Report › Report › Professional. TY - BOOK. T1 - Hilbert flag varieties and their Kähler structure In this paper we introduce the infinite-dimensional flag Cited by: 5. Flag Manifolds and Infinite Dimensional Kähler Geometry.

Abstract. Let G be a connected, compact Lie group, A (generalized) flag manifold for G is the quotient of G by the centralizer of a torus.

Hermitian symmetric spaces (e.g. complex projective spaces and Grassmannians), which are of the form G/C(T) for a circle T ⊂ G, are flag by: In this book we study three important classes of infinite-dimensional Kähler manifolds — loop spaces of compact Lie groups, Teichmüller spaces of complex structures on loop spaces, and Grassmannians of Hilbert spaces.

The study of Kähler immersions of a given real analytic Kähler manifold into a finite or infinite dimensional complex space form Cited by: We study analysis over infinite dimensional manifolds consisted by sequences of almost Kähler manifolds. In particular we develop moduli theory of pseudo holomorphic curves into the spaces with high symmetry.

As applications, we study Hamiltonian dynamics over the infinite dimensional manifolds, and induce some dynamical properties of Hamiltonian Author: Tsuyoshi Kato.

A Hermitian manifold is a complex manifold equipped with a metric g, such that gp(X, Y) = gp(JpX, JpY), where p ∈ M and X, Y ∈ TpM Again the web tells me that, J is a linear map between the tangent spaces at a point such that J2 = − 1. Lastly, the Kähler form ω is a tensor field whose action is given.

We construct a canonical Hausdorff complex analytic moduli space of Fano manifolds with Kähler-Ricci solitons. This naturally enlarges the moduli space of Fano manifolds with Kähler-Einstein metrics, which was constructed by Odaka and Li-Wang-Xu. We discover a moment map picture for Kähler-Ricci solitons, and give complex analytic charts on the topological space consisting of Kähler Cited by: 3.

Isometric submersions of Finsler manifolds. The notion of isometric submersion is extended to Finsler spaces and it is used to construct examples of Finsler metrics on complex and quater-nionic projective spaces all of whose geodesics are (geometrical) circles.

Notes [] ↑ The complex (including algebraic and Kähler) and symplectic only occur in even dimension; there are some odd-dimensional analogs. ↑ This level is suggestive: a Kähler manifold has all of these structures, and any two compatible such structures (with integrability conditions) yields an Kähler manifold.

↑ detailed distinction between geometry and topology. CiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): This thesis consists of three main results.

In the first one we describe all Kähler immersions of a bounded symmetric domain into the infinite dimensional complex pro-jective space in terms of the Wallach set of the domain. In the second one we exhibit an example of complete and non-homogeneous Kähler.

Homogeneous Kähler submanifolds of finite or infinite dimensional complex Euclidean form or hyperbolic space have been classified by Scala, Ishi, Loi in. The construction of complete nonhomogeneous Kähler–Einstein manifolds. In this section, we give the details of how to obtain a class of complete noncompact Kähler–Einstein by: 1.

It’s a Kähler manifold. And it’s that Kähler structure of L X L X which is responsible for the “chirality” of the string, i.e. the splitting into “left- and right-moving” parts of the maps S 1 → X S^1 \to X. Kähler manifolds are just what you want for geometric quantization.

A simple formula is given for the curvature of certain infinite dimensional homogeneous Kähler manifolds. In the case of Diff A T 2 C, C being the centralizer of some fixed area-preserving reparametrisation of the torus, the Ricci tensor diverges but yields zero when employing ζ-function regularisation; the same holds for some diffeomorphism groups of higher dimensional by: See there for pointers for how "convenient vector spaces" and hence the infinite-dimensional manifolds modeled on them ("convenient manifolds") are faithfully embedded into that topos.

In these toposes for instance all mapping spaces exist and can be usefully treated, while they agree with the infinite-dimensional manifold structures on mapping.In his book Mickelsson notices that the infinite-dimensional Grassmannian manifold of Segal and Wilson admits a Spin^c structure and after this he naturally considers the problem of defining a.