scholarly journals Codimension two Kähler submanifolds of space forms

2002 ◽  
Vol 79 (6) ◽  
pp. 520-528 ◽  
Author(s):  
M. J. Ferreira ◽  
R. Tribuzy
Keyword(s):  
Space Forms ◽  
Codimension Two ◽  
Kähler Submanifolds

scholarly journals Codimension two Kähler submanifolds of space forms

2002 ◽  
Vol 79 (6) ◽  
pp. 520-528
Author(s):  
M. J. Ferreira ◽  
R. Tribuzy
Keyword(s):  
Space Forms ◽  
Codimension Two ◽  
Kähler Submanifolds

scholarly journals Complete real Kähler submanifolds in codimension two

2007 ◽  
Vol 258 (2) ◽  
pp. 291-299 ◽  
Author(s):  
Luis A. Florit ◽  
Fangyang Zheng
Keyword(s):  
Codimension Two ◽  
Kähler Submanifolds

Constructing symplectic manifolds

2017 ◽  
Author(s):  
Dusa McDuff ◽  
Dietmar Salamon
Keyword(s):  
Final Section ◽  
Symplectic Manifolds ◽  
Homotopy Equivalence ◽  
Codimension Two ◽  
Open Manifolds ◽  
Connected Sums ◽  
Symplectic Forms ◽  
Ambient Manifold ◽  
Blowing Up ◽  
Four Manifolds

This chapter examines various ways to construct symplectic manifolds and submanifolds. It begins by studying blowing up and down in both the complex and the symplectic contexts. The next section is devoted to a discussion of fibre connected sums and describes Gompf’s construction of symplectic four-manifolds with arbitrary fundamental group. The chapter also contains an exposition of Gromov’s telescope construction, which shows that for open manifolds the h-principle rules and the inclusion of the space of symplectic forms into the space of nondegenerate 2-forms is a homotopy equivalence. The final section outlines Donaldson’s construction of codimension two symplectic submanifolds and explains the associated decompositions of the ambient manifold.

scholarly journals The ABCDEFG of little strings

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
Nathan Haouzi ◽  
Can Kozçaz
Keyword(s):  
Gauge Theory ◽  
Partition Function ◽  
Coulomb Gas ◽  
Conformal Block ◽  
Coulomb Branch ◽  
Quiver Gauge Theory ◽  
Codimension Two ◽  
Type Iib String Theory ◽  
Unified Description ◽  
Formula Type

Abstract Starting from type IIB string theory on an ADE singularity, the (2, 0) little string arises when one takes the string coupling gs to 0. In this setup, we give a unified description of the codimension-two defects of the little string, labeled by a simple Lie algebra $$ \mathfrak{g} $$ g . Geometrically, these are D5 branes wrapping 2-cycles of the singularity, subject to a certain folding operation when the algebra is non simply-laced. Equivalently, the defects are specified by a certain set of weights of $$ {}^L\mathfrak{g} $$ L g , the Langlands dual of $$ \mathfrak{g} $$ g . As a first application, we show that the instanton partition function of the $$ \mathfrak{g} $$ g -type quiver gauge theory on the defect is equal to a 3-point conformal block of the $$ \mathfrak{g} $$ g -type deformed Toda theory in the Coulomb gas formalism. As a second application, we argue that in the (2, 0) CFT limit, the Coulomb branch of the defects flows to a nilpotent orbit of $$ \mathfrak{g} $$ g .

Triharmonic Riemannian submersions from 3-dimensional space forms

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Tomoya Miura ◽  
Shun Maeta
Keyword(s):  
Existence Theorem ◽  
Space Form ◽  
Dimensional Space ◽  
Riemannian Submersion ◽  
Partial Answer ◽  
Riemannian Submersions ◽  
Space Forms ◽  
3 Dimensional

Abstract We show that any triharmonic Riemannian submersion from a 3-dimensional space form into a surface is harmonic. This is an affirmative partial answer to the submersion version of the generalized Chen conjecture. Moreover, a non-existence theorem for f -biharmonic Riemannian submersions is also presented.

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