scholarly journals Nonexistence of Certain Levi Flat Hypersurfaces in Kähler Manifolds from the Viewpoint of Positive Normal Bundles

2013 ◽  
Vol 49 (2) ◽  
pp. 229-239 ◽  
Author(s):  
Takeo Ohsawa
Keyword(s):  
Normal Bundles

The Development of Topological 4-manifold Theory

2021 ◽  
pp. 295-330
Author(s):  
Mark Powell ◽  
Arunima Ray
Keyword(s):  
Euclidean Space ◽  
Dimensional Euclidean Space ◽  
Smooth Structures ◽  
Normal Bundles ◽  
Exotic Smooth Structures ◽  
Poincare Conjecture ◽  
Manifold Theory ◽  
Simply Connected

The development of topological 4-manifold theory is described in the form of a flowchart showing the interdependence among many key statements in the theory. In particular, the flowchart demonstrates how the theory crucially relies on the constructions in this book, what goes into the work of Quinn on smoothing, normal bundles, and transversality, and what is needed to deduce the famous consequences, such as the classification of closed, simply connected, topological 4-manifolds, the category preserving Poincaré conjecture, and the existence of exotic smooth structures on 4-dimensional Euclidean space. Precise statements of the results, brief indications of some proofs, and extensive references are provided.

scholarly journals On a construction in bordism theory

1986 ◽  
Vol 29 (3) ◽  
pp. 413-422 ◽  
Author(s):  
Nigel Ray
Keyword(s):  
Line Bundles ◽  
Complex Line ◽  
Surgery Theory ◽  
Normal Bundles ◽  
Bordism Ring ◽  
Complex Line Bundles

In [2], R. Arthan and S. Bullett pose the problem of representing generators of the complex bordism ring MU* by manifolds which are totally normally split; i.e. whose stable normal bundles are split into a sum of complex line bundles. This has recently been solved by Ochanine and Schwartz [8] who use a mixture of J-theory and surgery theory to establish several results, including the following.

scholarly journals Normal bundles of rational curves on complete intersections

2019 ◽  
Vol 21 (02) ◽  
pp. 1850011 ◽  
Author(s):  
Izzet Coskun ◽  
Eric Riedl
Keyword(s):  
Complete Intersection ◽  
Normal Bundle ◽  
Rational Curves ◽  
Complete Intersections ◽  
Type Formula ◽  
Normal Bundles ◽  
Rationally Connected

Let [Formula: see text] be a general Fano complete intersection of type [Formula: see text]. If at least one [Formula: see text] is greater than [Formula: see text], we show that [Formula: see text] contains rational curves of degree [Formula: see text] with balanced normal bundle. If all [Formula: see text] are [Formula: see text] and [Formula: see text], we show that [Formula: see text] contains rational curves of degree [Formula: see text] with balanced normal bundle. As an application, we prove a stronger version of the theorem of Tian [27], Chen and Zhu [4] that [Formula: see text] is separably rationally connected by exhibiting very free rational curves in [Formula: see text] of optimal degrees.

Wavefront sets analysis of limited aperture migration sections

Geophysics ◽  
1991 ◽  
Vol 56 (6) ◽  
pp. 778-784 ◽  
Author(s):  
P. M. Carrion ◽  
H. K. Sato ◽  
A. V. D. Buono
Keyword(s):  
Relative Position ◽  
Real Data ◽  
Brazilian Coast ◽  
Data Set ◽  
Prestack Migration ◽  
Normal Bundles

Although geophysical literature is quite rich in papers on migration, there are only a few papers that treat LAM (Limited Aperture Migration). Deterministic and stochastic criteria for the reconstruction of reflection interfaces in prestack migration were derived and demonstrated on synthetic and real data examples (a real data set was acquired offshore the Brazilian coast, courtesy of Petrobras). The reconstruction of reflection interfaces in LAM depends on the relative position of “normal bundles,” as defined here, and gradients to the reflection interfaces. The derived stochastic criterion relates the variance of “normal bundles” to the variance of slowness in the medium. These criteria will help the geophysicist to identify directly distorted regions caused by LAM and those regions that are correctly migrated.

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