Invariant Kähler metrics and projective embeddings of the flag manifold

Kähler groups, quasi-projective groups and 3-manifold groups

We prove two results relating 3-manifold groups to fundamental groups occurring in complex geometry. Let N be a compact, connected, orientable 3-manifold. If N has non-empty, toroidal boundary, and π1(N) is a Kähler group, then N is the product of a torus with an interval. On the other hand, if N has either empty or toroidal boundary, and π1(N) is a quasi-projective group, then all the prime co...

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Finsler metrics of scalar flag curvature and projective invariants

In this paper, we define a new projective invariant and call it W̃ -curvature. We prove that a Finsler manifold with dimension n ≥ 3 is of constant flag curvature if and only if its W̃ -curvature vanishes. Various kinds of projectively flatness of Finsler metrics and their equivalency on Riemannian metrics are also studied. M.S.C. 2010: 53B40, 53C60.

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Classification of Embeddings of the Flag Geometries of Projective Planes in Finite Projective Spaces, Part 3

The flag geometry 1=(P, L, I) of a finite projective plane 6 of order s is the generalized hexagon of order (s, 1) obtained from 6 by putting P equal to the set of all flags of 6, by putting L equal to the set of all points and lines of 6, and where I is the natural incidence relation (inverse containment), i.e., 1 is the dual of the double of 6 in the sense of H. Van Maldeghem (1998, ``General...

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Classification of Embeddings of the Flag Geometries of Projective Planes in Finite Projective Spaces, Part 2

The flag geometry 1=(P, L, I) of a finite projective plane 6 of order s is the generalized hexagon of order (s, 1) obtained from 6 by putting P equal to the set of all flags of 6, by putting L equal to the set of all points and lines of 6, and where I is the natural incidence relation (inverse containment), i.e., 1 is the dual of the double of 6 in the sense of H. Van Maldeghem (1998, ``General...

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Classification of Embeddings of the Flag Geometries of Projective Planes in Finite Projective Spaces, Part 1

The flag geometry 1=(P, L, I) of a finite projective plane 6 of order s is the generalized hexagon of order (s, 1) obtained from 6 by putting P equal to the set of all flags of 6, by putting L equal to the set of all points and lines of 6, and where I is the natural incidence relation (inverse containment), i.e., 1 is the dual of the double of 6 in the sense of H. Van Maldeghem (1998, ``General...

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Invariant Kähler metrics and projective embeddings of the flag manifold

نویسندگان

چکیده

منابع مشابه

Kähler groups, quasi-projective groups and 3-manifold groups

Finsler metrics of scalar flag curvature and projective invariants

Classification of Embeddings of the Flag Geometries of Projective Planes in Finite Projective Spaces, Part 3

Classification of Embeddings of the Flag Geometries of Projective Planes in Finite Projective Spaces, Part 2

Classification of Embeddings of the Flag Geometries of Projective Planes in Finite Projective Spaces, Part 1

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