Ruled special Lagrangian surfaces

Borisenko, Alexander A.

doi:10.1090/advsov/015/08

Cited by 11 publications

(25 citation statements)

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“…Borisenko [1] generalized this result by adding a harmonic function to the case when M is a minimal surface in R 3 .…”

Section: Normal Bundle Of An Austere Manifoldmentioning

confidence: 98%

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Weighted area-minimizing submanifolds with soap-film-like singularities assembled from special Lagrangian pieces

Doan

2010

Sci. China Math.

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A sufficient condition for a set of calibrated submanifolds to be area-minimizing with multiplicities, also call weighted area-minimizing under diffeomorphisms (WAMD) is stated. We construct some WAMD submanifolds by assembling pieces of special Lagrangian (SL) normal bundles including the one of three surfaces meeting at an angle of 120 • along soap-film-like singularities. We also mention a symmetry property of SL submanifolds and Björling type problem for SL normal bundles. Keywordsweighted area-minimizing under diffeomorphisms, special Lagrangian MSC(2000): Primary 49Q05; Secondary 53A10, 58E12Citation: Hieu D T. Weighted area-minimizing submanifolds with soap-film-like singularities assembled from special

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“…Borisenko [1] generalized this result by adding a harmonic function to the case when M is a minimal surface in R 3 .…”

Section: Normal Bundle Of An Austere Manifoldmentioning

confidence: 98%

“…For details about SL normal bundles we refer the reader to [1] and [7]. For some WAMD examples of polyhedral sets and the first ones of non-flat sheets meeting along multiple curves at an equal angle, see [8].…”

Section: Sl Normal Bundle Examplesmentioning

confidence: 99%

Weighted area-minimizing submanifolds with soap-film-like singularities assembled from special Lagrangian pieces

Doan

2010

Sci. China Math.

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“…Joyce in [2][3][4][5] gave explicit examples of special Lagrangian submanifolds in C n . Borisenko [6] constructed a lot of twisted special Lagrangian submanifolds in T * R 3 from the twisted normal bundle of minimal surfaces given in R 3 . This is a generalization of normal bundle given in [1] with dimension 3.…”

Section: §1 Introductionmentioning

confidence: 99%

“…This is a generalization of normal bundle given in [1] with dimension 3. Bryant [7] gave a class of twisted special Lagrangian submanifolds in C 3 , which are different from the ones in [6].Austere is also a special kind of minimal submanifold, which were first given in [1]. In recent years, there are some people who study these submanifolds.…”

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confidence: 99%

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New construction of special Lagrangian submanifolds in T*R n equipped with the standard metric

Han

2008

Appl. Math. J. Chin. Univ.

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A class of twisted special Lagrangian submanifolds in T * R n and a kind of austere submanifold from conormal bundle of minimal surface of R 3 are constructed. §1 Introduction Special Lagrangian sumbmanifolds may be defined as those submanifolds which are both Lagrangian and minimal. Alternatively, they are characterised as those submnaifolds which are calibrated by a certain n-form, so they have the remarkable property of being area minimizing. These submanifolds have received many attention recently due to connection with string theory. More particularly, understanding fibration of special Lagrangian in Calabi-Yau manifolds of dimension 3 is crucial for mirror symmetry. Examples of special Lagrangian submanifolds are very important for studying these submanifolds. In recent years, some examples of these submanifolds have been constructed by many people. For example, Harvey and Lawson [1] gave some examples of special Lagrangian sumbmanifolds in C n , and especially they constructed a class of special Lagrangian submanifolds by using normal bundles. Joyce in [2][3][4][5] gave explicit examples of special Lagrangian submanifolds in C n . Borisenko [6] constructed a lot of twisted special Lagrangian submanifolds in T * R 3 from the twisted normal bundle of minimal surfaces given in R 3 . This is a generalization of normal bundle given in [1] with dimension 3. Bryant [7] gave a class of twisted special Lagrangian submanifolds in C 3 , which are different from the ones in [6].Austere is also a special kind of minimal submanifold, which were first given in [1]. In recent years, there are some people who study these submanifolds. For example, Brant [8] , Dajczer and Florit [9] gave many properties of these submanifolds. Harvay and Lawson [1] gave some special Lagrangian submanifold by using austere submanifolds.In this paper, we construct a kind of twisted special Lagrangian submanifolds in T * R n from the twisted normal bundle of minimal surfaces in R n , and this is a generalization of the case given in [6] in higher dimension. We also find a kind of austere submanifold in C 3 = R 6 , and then get a lot of special Lagrangian submanifolds in T * R 6 . §2 Preliminaries We begin by defining calibration and calibrated submanifolds, following Harvay and Lawson [1] .

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Nonexistence of minimal Lagrangian spheres in hyperKähler manifolds

Smoczyk¹

2000

Calc Var

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Ruled special Lagrangian surfaces

Cited by 11 publications

References 0 publications

Weighted area-minimizing submanifolds with soap-film-like singularities assembled from special Lagrangian pieces

Weighted area-minimizing submanifolds with soap-film-like singularities assembled from special Lagrangian pieces

New construction of special Lagrangian submanifolds in T*R n equipped with the standard metric

Nonexistence of minimal Lagrangian spheres in hyperKähler manifolds

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