scholarly journals Normal-Bundle Bootstrap

2021 ◽  
Vol 3 (2) ◽  
pp. 573-592
Author(s):  
Ruda Zhang ◽  
Roger Ghanem
Keyword(s):  
Normal Bundle

Anyon Networks from Geometric Models of Matter

2021 ◽  
Author(s):  
Michael Atiyah ◽  
Matilde Marcolli
Keyword(s):  
Normal Bundle ◽  
Present Form ◽  
Joint Work ◽  
Geometric Models ◽  
Tensor Networks

Abstract This paper, completed in its present form by the second author after the first author passed away in 2019, describes an intended continuation of the previous joint work on anyons in geometric models of matter. This part outlines a construction of anyon tensor networks based on four-dimensional orbifold geometries and braid representations associated with surface-braids defined by multisections of the orbifold normal bundle of the surface of orbifold points.

Submanifolds of ? N with splitting normal bundle sequence are linear

1978 ◽  
Vol 234 (3) ◽  
pp. 253-261 ◽  
Author(s):  
J. Morrow ◽  
H. Rossi
Keyword(s):  
Normal Bundle

scholarly journals KODAIRA DIMENSION OF SUBVARIETIES II

2006 ◽  
Vol 17 (05) ◽  
pp. 619-631 ◽  
Author(s):  
THOMAS PETERNELL
Keyword(s):  
Normal Bundle ◽  
General Type ◽  
Kodaira Dimension ◽  
Projective Manifold ◽  
Fundamental Groups ◽  
Weak Version ◽  
Joint Paper ◽  
Rationally Connected

This paper continues the study of non-general type subvarieties begun in a joint paper with Schneider and Sommese [14]. We prove uniruledness of a projective manifold containing a submanifold not of general type whose normal bundle has positivity properties and study moreover the rational quotient. We also relate the fundamental groups and a prove a cohomological criterion for a manifold to be rationally connected (weak version of a conjecture of Mumford).

Stein manifolds of nonnegative curvature

2018 ◽  
Vol 18 (3) ◽  
pp. 285-287
Author(s):  
Xiaoyang Chen
Keyword(s):  
Fixed Point ◽  
Sectional Curvature ◽  
Normal Bundle ◽  
Stein Manifold ◽  
Riemannian Metric ◽  
Nonnegative Curvature ◽  
Fixed Point Set ◽  
Nonnegative Sectional Curvature ◽  
Point Set ◽  
Nonempty Compact

AbstractLet X bea Stein manifold with an anti-holomorphic involution τ and nonempty compact fixed point set Xτ. We show that X is diffeomorphic to the normal bundle of Xτ provided that X admits a complete Riemannian metric g of nonnegative sectional curvature such that τ*g = g.

Rational Integer Invariants of Regular Cyclic Actions

2004 ◽  
Vol 47 (1) ◽  
pp. 60-72 ◽  
Author(s):  
Robert D. Little
Keyword(s):  
Fixed Point ◽  
Normal Bundle ◽  
Complex Structure ◽  
Rational Integer ◽  
Fixed Point Set ◽  
Cyclic Action ◽  
Point Set ◽  
Smooth Map

AbstractLet g : M2n → M2n be a smooth map of period m ≥ 2 which preserves orientation. Suppose that the cyclic action defined by g is regular and that the normal bundle of the fixed point set F has a g-equivariant complex structure. Let F ⋔ F be the transverse self-intersection of F with itself. If the g-signature Sign(g, M) is a rational integer and n < ϕ(m), then there exists a choice of orientations such that Sign(g, M) = Sign F = Sign(F ⋔ F).

scholarly journals ADJUNCTION FOR VARIETIES WITH A ℂ* ACTION

2020 ◽  
Author(s):  
ELEONORA A. ROMANO ◽  
JAROSŁAW A. WIŚNIEWSKI
Keyword(s):  
Fixed Point ◽  
Line Bundle ◽  
Normal Bundle ◽  
Ample Line Bundle ◽  
Projective Manifold ◽  
Fano Manifolds ◽  
Adjunction Theory ◽  
Rank 2 ◽  
General Orbit ◽  
Complex Projective

Abstract Let X be a complex projective manifold, L an ample line bundle on X, and assume that we have a ℂ* action on (X;L). We classify such triples (X; L;ℂ*) for which the closure of a general orbit of the ℂ* action is of degree ≤ 3 with respect to L and, in addition, the source and the sink of the action are isolated fixed points, and the ℂ* action on the normal bundle of every fixed point component has weights ±1. We treat this situation by relating it to the classical adjunction theory. As an application, we prove that contact Fano manifolds of dimension 11 and 13 are homogeneous if their group of automorphisms is reductive of rank ≥ 2.

Normal and osculating maps for submanifolds of RN

1990 ◽  
Vol 114 (1-2) ◽  
pp. 39-55 ◽  
Author(s):  
I. Cattaneo Gasparini ◽  
G. Romani
Keyword(s):  
Isometric Immersion ◽  
Normal Bundle ◽  
Necessary Conditions ◽  
Sufficient Conditions ◽  
Gauss Map ◽  
Necessary And Sufficient Conditions ◽  
Totally Geodesic ◽  
Precise Formulation ◽  
Parallel Case ◽  
Necessary And Sufficient

SynopsisLet Mn be a manifold supposed “nicely curved” isometrically immersed in ℝn+p. Starting from a generalised Gauss map associated to the splitting of the normal bundle defined from the values of the fundamental forms of M of order k (k ≧ 0), we give necessary and sufficient conditions for the map to be totally geodesic and harmonic . For k = 0 is the classical Gauss map and our formula reduces to Ruh–Vilm's formula with a more precise formulation due to the consideration of the splitting of the normal bundle.We also give necessary conditions for M, supposed complete, to admit an isometric immersion with . This theorem generalises a theorem of Vilms on the manifolds with second fundamental forms parallel (case k = 0). The result is interesting as the class of manifolds satisfying the condition is larger than the class of manifolds satisfying .

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