Nonnegatively curved Euclidean submanifolds in codimension two

Luis Florit; Wolfgang Ziller

doi:10.4171/cmh/398

Nonnegatively curved Euclidean submanifolds in codimension two

Commentarii Mathematici Helvetici ◽

10.4171/cmh/398 ◽

2016 ◽

Vol 91 (4) ◽

pp. 629-651 ◽

Cited By ~ 1

Author(s):

Luis Florit ◽

Wolfgang Ziller

Keyword(s):

Codimension Two ◽

Euclidean Submanifolds

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Genuine Rigidity of Euclidean Submanifolds in Codimension Two

Geometriae Dedicata ◽

10.1023/b:geom.0000033846.63094.46 ◽

2004 ◽

Vol 106 (1) ◽

pp. 195-210 ◽

Cited By ~ 7

Author(s):

Marcos Dajczer ◽

Luis A. Florit

Keyword(s):

Codimension Two ◽

Euclidean Submanifolds

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Submanifolds of codimension two attaining equality in an extrinsic inequality

Mathematical Proceedings of the Cambridge Philosophical Society ◽

10.1017/s0305004108001813 ◽

2009 ◽

Vol 146 (2) ◽

pp. 461-474 ◽

Cited By ~ 12

Author(s):

MARCOS DAJCZER ◽

RUY TOJEIRO

Keyword(s):

Scalar Curvature ◽

Curvature Tensor ◽

Minimal Surfaces ◽

Mean Curvature ◽

Arbitrary Dimension ◽

Curvature Vector ◽

Mean Curvature Vector ◽

Codimension Two ◽

The Mean ◽

Euclidean Submanifolds

AbstractWe provide a parametric construction in terms of minimal surfaces of the Euclidean submanifolds of codimension two and arbitrary dimension that attain equality in an inequality due to De Smet, Dillen, Verstraelen and Vrancken. The latter involves the scalar curvature, the norm of the normal curvature tensor and the length of the mean curvature vector.

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Constructing symplectic manifolds

10.1093/oso/9780198794899.003.0008 ◽

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.

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The ABCDEFG of little strings

Journal of High Energy Physics ◽

10.1007/jhep06(2021)092 ◽

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 .

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