7 edition of **The classification of three-dimensional homogeneous complex manifolds** found in the catalog.

- 232 Want to read
- 22 Currently reading

Published
**1995**
by Springer in Berlin, New York
.

Written in English

- Homogeneous complex manifolds

**Edition Notes**

Includes bibliographical references (p. [225]-228) and index.

Statement | Jörg Winkelmann. |

Series | Lecture notes in mathematics ;, 1602, Lecture notes in mathematics (Springer-Verlag) ;, 1602. |

Classifications | |
---|---|

LC Classifications | QA3 .L28 no. 1602, QA613.2 .L28 no. 1602 |

The Physical Object | |

Pagination | xi, 230 p. : |

Number of Pages | 230 |

ID Numbers | |

Open Library | OL1272750M |

ISBN 10 | 3540590722 |

LC Control Number | 95004081 |

[7] G. Calvaruso, Four-dimensional paraKähler Lie algebras: classification and geometry, Houston J. Math., to appear. Google Scholar [8] G. Calvaruso and A. Fino, Complex and paracomplex structures on homogeneous pseudo-Riemannian four-manifolds, Int. J. Math., 24 (), , 28 pp. Crossref Web of Science Google Scholar. We study the reduction procedure applied to pseudo-Kähler manifolds by a one dimensional Lie group acting by isometries and preserving the complex tensor. We endow the quotient manifold with an almost contact metric structure. We use this fact to connect pseudo-Kähler homogeneous structures with almost contact metric homogeneous structures. .

This is a local condition which has to be satisfied at all points, and in this way it is a generalization of E. Cartan's method for symmetric spaces. The main aim of the authors is to use this theorem and representation theory to give a classification of homogeneous . In mathematics, low-dimensional topology is the branch of topology that studies manifolds, or more generally topological spaces, of four or fewer entative topics are the structure theory of 3-manifolds and 4-manifolds, knot theory, and braid can be regarded as a part of geometric may also be used to refer to the study of .

One example of a three-dimensional Calabi–Yau manifold is a non-singular quintic threefold in CP 4, which is the algebraic variety consisting of all of the zeros of a homogeneous quintic polynomial in the homogeneous coordinates of the CP 4. Another example is a smooth model of the Barth–Nieto quintic. Implications of complex structure. Since holomorphic functions are much more rigid than smooth functions, the theories of smooth and complex manifolds have very different flavors: compact complex manifolds are much closer to algebraic varieties than to differentiable manifolds.. For example, the Whitney embedding theorem tells us that every smooth n-dimensional manifold .

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This book provides a classification of all three-dimensional complex manifolds for which there exists a transitive action (by biholomorphic transformations) of a real Lie group.

This means two homogeneous complex manifolds are considered equivalent if they are isomorphic as complex manifolds. The Classification of Three-dimensional Homogeneous Complex Manifolds by Jörg Winkelmann.

By Jörg Winkelmann. The Classification of Three-dimensional Homogeneous Complex Manifolds. New York: Springer-Verlag, Paperback. pages. x inches. Like new Rating: % positive. Survey.- The classification of three-dimensional homogeneous complex manifolds X=G/H where G is a complex lie group.- The classification of three-dimensional homogeneous complex manifolds X=G/H where G is a real lie group.

Series Title: Lecture notes in mathematics, Responsibility: Jörg Winkelmann. More information: Inhaltstext; catdir.

Survey.- The classification of three-dimensional homogeneous complex manifolds X=G/H where G is a complex lie group.- The classification of three-dimensional homogeneous complex manifolds X=G/H where G is a real lie group. Series Title: Lecture notes in mathematics (Springer-Verlag), Responsibility: Jörg Winkelmann.

The classification of three-dimensional complex-homogeneous manifolds was completed in [W1]. Finally in the general classification of the three-dimensional homogeneous complex manifolds was given by our Dissertation [W2].

The purpose of this note is to describe these manifolds and briefly outline the methods involved in the Cited by: Cite this chapter as: Winkelmann J. () The classification of three-dimensional homogeneous complex manifolds X=G/H where G is a complex lie group.

In: The Classification of Three-Dimensional Homogeneous Complex by: The Classification of Three-dimensional Homogeneous Complex Manifolds Springer. Contents PARTI Survey Survey 2 Introduction 2 The complete List 2 G r*a-[i~ir aolvable 2 G complex aemisimple 3 G complex mized 3 G real aolvable 5 G real non-solvable 7.

In this study, we apply a result of H. Wang and Hano-Kobayashi on the classification of compact complex homogeneous manifolds with a compact reductive Lie group to give some more homogeneous. Winkelmann classified all three-dimensional homogeneous complex manifolds in.

In particular, he discovered a domain that is bounded by the Levi-indefinite hypersurface Im (w + z 1 z ¯ 2) = | z 1 | 4, where (z 1, z 2, w) are coordinates in C 3. This hypersurface features the largest possible symmetry algebra among the non-quadratic hypersurfaces.

Formally, classifying manifolds is classifying objects up to are many different notions of "manifold", and corresponding notions of "map between manifolds", each of which yields a different category and a different classification question.

These categories are related by forgetful functors: for instance, a differentiable manifold is also a topological manifold, and a. In this paper we completely classify the linearly full homogeneous holomorphic two-spheres in the complex Grassmann manifolds G (2, N) and G (3, N).We also obtain the Gauss equation for the holomorphic immersions from a Riemann surface into G (k, N).By using which, we give explicit expressions of the Gaussian curvature and the square of the length of.

Cite this chapter as: Winkelmann J. () Survey. In: The Classification of Three-Dimensional Homogeneous Complex Manifolds.

Lecture. In this paper we study three dimensional homogeneous Finsler manifolds. We first obtain a complete list of the three-dimensional homogeneous manifolds.

The purpose of this paper is to classify all simply connected homogeneous almost cosymplectic three-manifolds. We show that each such three-manifold is either a Lie group G equipped with a left invariant almost cosymplectic structure or a Riemannian product of type R × N, where N is a Kähler surface of constant curvature.

Moreover, we find that the Reeb vector field of any homogeneous. A pleasant feature of 3 manifolds, in contrast to higher dimensions, is that there is no essential diﬀerence between smooth, piecewise linear, and topological mani-folds.

It was shown by Bing and Moise in the s that every topological 3-manifold can be triangulated as a simplicial complex whose combinatorial type is unique up to subdivision. Geometry of homogeneous spaces.

According to F. Klein's Erlangen program, the subject of the geometry of a homogeneous space is the study of invariants of the group of motions of a homogeneous classical area of research here is the classification of the various subsets of a homogeneous space, in particular submanifolds and their unions, families of.

The classification of three-dimensional homogeneous complex manifolds: Complex analytic geometry of complex parallelizable manifolds: n Nevanlinna theory in several complex variables and diophantine approximation.

Taking into account the classification of three-dimensional Riemannian Lie groups given by Milnor, this result permits one to determine all three-dimensional homogeneous Riemannian manifolds. To our knowledge, while several interesting examples of three-dimensional homogeneous Lorentzian manifolds are known [3], [8], [14], [15], a.

In mathematics, particularly in the theories of Lie groups, algebraic groups and topological groups, a homogeneous space for a group G is a non-empty manifold or topological space X on which G acts elements of G are called the symmetries of X.A special case of this is when the group G in question is the automorphism group of the space X – here "automorphism.

6. Three-dimensional homogeneous contact Lorentzian manifolds. To complete the classification of contact pseudo-metric manifolds of constant sectional curvature and to find some relevant non-Sasakian examples, we shall classify all three-dimensional homogeneous contact pseudo-metric manifolds.

Classification of three-dimensional homogeneous complex manifolds. Berlin ; New York: Springer, © (DLC) Material Type: Document, Internet resource: Document Type: Internet Resource, Computer File: All Authors / Contributors: Jörg Winkelmann.The classification of three-dimensional complex-homogeneous manifolds was completed in [W1].

Finally in the general classification of the three-dimensional homogeneous complex manifolds.The classification of three-dimensional homogeneous complex manifolds. Springer／c 当館請求記号：MAA