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Warped compact foliations

Szymon M. Walczak (2008)

Annales Polonici Mathematici

The notion of the Hausdorffized leaf space ˜ of a foliation is introduced. A sufficient condition for warped compact foliations to converge to ˜ is given. Moreover, a necessary condition for warped compact Hausdorff foliations to converge to ˜ is shown. Finally, some examples are examined.

Warped Product CR-Submanifolds in Lorentzian para Sasakian Manifolds

Uddin, Siraj (2010)

Serdica Mathematical Journal

2000 Mathematics Subject Classification: 53C15, 53C40, 53C42.Many research articles have recently appeared exploring existence or non existence of warped product submanifolds in known spaces (cf. [2, 5, 8]). The objective of the present paper is to study the existence or non-existence of contact CR-warped products in the setting of LP-Sasakian manifolds.This work is supported by the research grant RG117/10AFR (University of Malaya).

Warped Product Semi-Slant Submanifolds of a Sasakian Manifold

Al-Solamy, Falleh R., Khan, Viqar Azam (2008)

Serdica Mathematical Journal

2000 Mathematics Subject Classification: 53C40, 53C25.In the present note, it is proved that there donot exist warped product semi-slant submanifolds in a Sasakian manifold other than contact CR-warped product submanifolds and thus the results obtained in [8] are generalized.

Warped product submanifolds of Kaehler manifolds with a slant factor

Bayram Sahin (2009)

Annales Polonici Mathematici

Recently, we showed that there exist no warped product semi-slant submanifolds in Kaehler manifolds. On the other hand, Carriazo introduced anti-slant submanifolds as a particular class of bi-slant submanifolds. In this paper, we study such submanifolds in detail and show that they are useful to define a new kind of warped product submanifolds of Kaehler manifolds. In this direction, we obtain the existence of warped product hemi-slant (anti-slant) submanifolds with examples. We give a characterization...

Weak and strong density results for the Dirichlet energy

Mariano Giaquinta, Domenico Mucci (2004)

Journal of the European Mathematical Society

Let 𝒴 be a smooth oriented Riemannian manifold which is compact, connected, without boundary and with second homology group without torsion. In this paper we characterize the sequential weak closure of smooth graphs in B n × 𝒴 with equibounded Dirichlet energies, B n being the unit ball in n . More precisely, weak limits of graphs of smooth maps u k : B n 𝒴 with equibounded Dirichlet integral give rise to elements of the space cart 2 , 1 ( B n × 𝒴 ) (cf. [4], [5], [6]). In this paper we prove that every element T in cart 2 , 1 ( B n × 𝒴 ) is the weak limit...

Weak symplectic fillings and holomorphic curves

Klaus Niederkrüger, Chris Wendl (2011)

Annales scientifiques de l'École Normale Supérieure

We prove several results on weak symplectic fillings of contact 3 -manifolds, including: (1) Every weak filling of any planar contact manifold can be deformed to a blow up of a Stein filling. (2) Contact manifolds that have fully separating planar torsion are not weakly fillable—this gives many new examples of contact manifolds without Giroux torsion that have no weak fillings. (3) Weak fillability is preserved under splicing of contact manifolds along symplectic pre-Lagrangian tori—this gives many...

Weakly irreducible subgroups of Sp ( 1 , n + 1 )

Natalia I. Bezvitnaya (2008)

Archivum Mathematicum

Connected weakly irreducible not irreducible subgroups of Sp ( 1 , n + 1 ) SO ( 4 , 4 n + 4 ) that satisfy a certain additional condition are classified. This will be used to classify connected holonomy groups of pseudo-hyper-Kählerian manifolds of index 4.

Weakly regular T 2 -symmetric spacetimes. The global geometry of future Cauchy developments

Philippe LeFloch, Jacques Smulevici (2015)

Journal of the European Mathematical Society

We provide a geometric well-posedness theory for the Einstein equations within the class of weakly regular vacuum spacetimes with T 2 -symmetry, as defined in the present paper, and we investigate their global causal structure. Our assumptions allow us to give a meaning to the Einstein equations under weak regularity as well as to solve the initial value problem under the assumed symmetry. First, introducing a frame adapted to the symmetry and identifying certain cancellation properties taking place...

Weakly-Einstein hermitian surfaces

Vestislav Apostolov, Oleg Muškarov (1999)

Annales de l'institut Fourier

A consequence of the Riemannian Goldberg-Sachs theorem is the fact that the Kähler form of an Einstein Hermitian surface is an eigenform of the curvature operator. Referring to this property as * -Einstein condition we obtain a complete classification of the compact locally homogeneous * -Einstein Hermitian surfaces. We also provide large families of non-homogeneous * -Einstein (but non-Einstein) Hermitian metrics on 2 2 , 1 × 1 , and on the product surface X × Y of two curves X and Y whose genuses are greater...

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