A note on complex projective threefolds admitting holomorphic contact structures

1994 ◽  
Vol 115 (1) ◽  
pp. 311-314 ◽  
Author(s):  
Yun-Gang Ye
Keyword(s):  
Contact Structures ◽  
Projective Threefolds ◽  
Complex Projective ◽  
Holomorphic Contact

CHARACTERIZATIONS OF BERGER SPHERES FROM THE VIEWPOINT OF SUBMANIFOLD THEORY

2019 ◽  
Vol 62 (1) ◽  
pp. 137-145 ◽  
Author(s):  
BYUNG HAK KIM ◽  
IN-BAE KIM ◽  
SADAHIRO MAEDA
Keyword(s):  
Projective Space ◽  
Complex Projective Space ◽  
Contact Structures ◽  
Real Hypersurfaces ◽  
Berger Spheres ◽  
Geodesic Spheres ◽  
Complex Projective

AbstractIn this paper, Berger spheres are regarded as geodesic spheres with sufficiently big radii in a complex projective space. We characterize such real hypersurfaces by investigating their geodesics and contact structures from the viewpoint of submanifold theory.

scholarly journals Some results on equivariant contact geometry for partial flag varieties

2016 ◽  
Vol 27 (08) ◽  
pp. 1650066 ◽  
Author(s):  
Peter Crooks ◽  
Steven Rayan
Keyword(s):  
Vector Bundles ◽  
Contact Structures ◽  
Flag Varieties ◽  
Contact Manifolds ◽  
Projective Varieties ◽  
Simply Connected ◽  
Complex Projective ◽  
Special Case ◽  
Partial Flag Varieties

We study equivariant contact structures on complex projective varieties arising as partial flag varieties [Formula: see text], where [Formula: see text] is a connected, simply-connected complex simple group of type ADE and [Formula: see text] is a parabolic subgroup. We prove a special case of the LeBrun-Salamon conjecture for partial flag varieties of these types. The result can be deduced from Boothby’s classification of compact simply-connected complex contact manifolds with transitive action by contact automorphisms, but our proof is completely independent and relies on properties of [Formula: see text]-equivariant vector bundles on [Formula: see text]. A byproduct of our argument is a canonical, global description of the unique [Formula: see text]-invariant contact structure on the isotropic Grassmannian of 2-planes in [Formula: see text].

Threefolds in ℙ6 of degree 12

2015 ◽  
Vol 15 (2) ◽  
Author(s):  
Marina Bertolini ◽  
Cristina Turrini
Keyword(s):  
Normal Complex ◽  
Projective Threefolds ◽  
Complex Projective

AbstractLinearly normal complex projective threefolds of degree 12, embedded in ℙ

On submersions of the complex indicatrix

Filomat ◽  
2017 ◽  
Vol 31 (16) ◽  
pp. 5081-5092
Author(s):  
Elena Popovicia
Keyword(s):  
Fixed Point ◽  
Complex Projective Space ◽  
Finsler Space ◽  
Hermitian Manifold ◽  
Almost Hermitian Manifold ◽  
Codimension One ◽  
Real Submanifold ◽  
Fundamental Equations ◽  
Complex Projective ◽  
Extrinsic Sphere

In this paper we study the complex indicatrix associated to a complex Finsler space as an embedded CR - hypersurface of the holomorphic tangent bundle, considered in a fixed point. Following the study of CR - submanifolds of a K?hler manifold, there are investigated some properties of the complex indicatrix as a real submanifold of codimension one, using the submanifold formulae and the fundamental equations. As a result, the complex indicatrix is an extrinsic sphere of the holomorphic tangent space in each fibre of a complex Finsler bundle. Also, submersions from the complex indicatrix onto an almost Hermitian manifold and some properties that can occur on them are studied. As application, an explicit submersion onto the complex projective space is provided.

Autonomous Geometrical Mechanics

2018 ◽  
Author(s):  
Peter Mann
Keyword(s):  
Phase Space ◽  
Contact Structure ◽  
Invariant Tori ◽  
Time Dependent ◽  
Contact Structures ◽  
Natural Setting ◽  
Adiabatic Invariance ◽  
Jet Bundle ◽  
Integrability Theorem ◽  
Extended Phase

This chapter examines the structure of the phase space of an integrable system as being constructed from invariant tori using the Arnold–Liouville integrability theorem, and periodic flow and ergodic flow are investigated using action-angle theory. Time-dependent mechanics is formulated by extending the symplectic structure to a contact structure in an extended phase space before it is shown that mechanics has a natural setting on a jet bundle. The chapter then describes phase space of integrable systems and how tori behave when time-dependent dynamics occurs. Adiabatic invariance is discussed, as well as slow and fast Hamiltonian systems, the Hannay angle and counter adiabatic terms. In addition, the chapter discusses foliation, resonant tori, non-resonant tori, contact structures, Pfaffian forms, jet manifolds and Stokes’s theorem.

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