scholarly journals Twistorial construction of minimal hypersurfaces

2014 ◽  
Vol 11 (06) ◽  
pp. 1450064 ◽  
Author(s):  
Johann Davidov
Keyword(s):  
Twistor Space ◽  
Riemannian Metric ◽  
Hermitian Structure ◽  
Complex Structures ◽  
Minimal Hypersurfaces ◽  
Almost Hermitian Structure

Every almost Hermitian structure (g, J) on a four-manifold M determines a hypersurface ΣJ in the (positive) twistor space of (M, g) consisting of the complex structures anti-commuting with J. In this paper, we find the conditions under which ΣJ is minimal with respect to a natural Riemannian metric on the twistor space in the cases when J is integrable or symplectic. Several examples illustrating the obtained results are also discussed.

Riemannian-polarized k-symplectic manifolds

2021 ◽  
Vol 18 (12) ◽  
Author(s):  
Ismail Benali ◽  
Souhaila Elamine ◽  
Azzouz Awane
Keyword(s):  
Symplectic Structure ◽  
Complex Structure ◽  
Riemannian Metric ◽  
Symplectic Manifolds ◽  
Complex Case ◽  
Hermitian Structure ◽  
Complex Structures ◽  
Dimensional Manifold ◽  
Almost Complex

In this paper, we give an analogue of the Hermitian structure in the almost complex case, on an [Formula: see text]-dimensional manifold endowed with an almost [Formula: see text]-complex metric. Also, we study the compatibility between Riemannian metric and polarized [Formula: see text]-symplectic structure. Also, we study some properties of an almost [Formula: see text]-complex structure. Moreover, we give an equivalence between almost [Formula: see text]-complex structures, [Formula: see text]-almost tangent structures and [Formula: see text]-almost cotangent structures.

scholarly journals Compatible complex structures on twistor space

2011 ◽  
Vol 61 (6) ◽  
pp. 2219-2248 ◽  
Author(s):  
Guillaume Deschamps
Keyword(s):  
Twistor Space ◽  
Complex Structures

scholarly journals Integrable Complex Structures on Twistor Spaces

2019 ◽  
Vol 70 (3) ◽  
pp. 937-963
Author(s):  
Steven Gindi
Keyword(s):  
Twistor Space ◽  
Complex Structures ◽  
Complex Manifolds ◽  
Twistor Spaces

Abstract We introduce integrable complex structures on twistor spaces fibered over complex manifolds. We then show, in particular, that the twistor spaces associated with generalized Kahler, SKT and strong HKT manifolds all naturally admit complex structures. Moreover, in the strong HKT case, we construct a metric and three compatible complex structures on the twistor space that have equal torsions.

scholarly journals Almost Hermitian structure on $S^6$

1955 ◽  
Vol 7 (3) ◽  
pp. 151-156 ◽  
Author(s):  
Tetsuzo Fukami ◽  
Shigeru Ishihara
Keyword(s):  
Hermitian Structure ◽  
Almost Hermitian Structure

scholarly journals Min–max theory for free boundary minimal hypersurfaces II: general Morse index bounds and applications

2020 ◽  
Author(s):  
Qiang Guang ◽  
Martin Man-chun Li ◽  
Zhichao Wang ◽  
Xin Zhou
Keyword(s):  
Free Boundary ◽  
Compact Manifold ◽  
Morse Index ◽  
Riemannian Metric ◽  
Upper Bounds ◽  
Minimal Hypersurfaces ◽  
Manifold With Boundary ◽  
Boundary Setting ◽  
Mean Convex ◽  
Convex Point

Abstract For any smooth Riemannian metric on an $$(n+1)$$ ( n + 1 ) -dimensional compact manifold with boundary $$(M,\partial M)$$ ( M , ∂ M ) where $$3\le (n+1)\le 7$$ 3 ≤ ( n + 1 ) ≤ 7 , we establish general upper bounds for the Morse index of free boundary minimal hypersurfaces produced by min–max theory in the Almgren–Pitts setting. We apply our Morse index estimates to prove that for almost every (in the $$C^\infty $$ C ∞ Baire sense) Riemannan metric, the union of all compact, properly embedded free boundary minimal hypersurfaces is dense in M. If $$\partial M$$ ∂ M is further assumed to have a strictly mean convex point, we show the existence of infinitely many compact, properly embedded free boundary minimal hypersurfaces whose boundaries are non-empty. Our results prove a conjecture of Yau for generic metrics in the free boundary setting.

CURVATURE AND INTEGRABILITY OF AN ALMOST HERMITIAN STRUCTURE

2006 ◽  
Vol 17 (01) ◽  
pp. 97-105 ◽  
Author(s):  
ZIZHOU TANG
Keyword(s):  
Necessary Conditions ◽  
Frame Theory ◽  
Hermitian Structure ◽  
Moving Frame ◽  
Almost Hermitian Structure

By using moving frame theory, we obtain some necessary conditions involving curvatures for integrability of an almost Hermitian structure. As consequences, they are applied to S6.

Harmonicity of proper almost complex structures on Walker 4-manifolds

2017 ◽  
Vol 14 (06) ◽  
pp. 1750094
Author(s):  
Johann Davidov ◽  
Absar Ul-Haq ◽  
Oleg Mushkarov
Keyword(s):  
Twistor Space ◽  
Harmonic Map ◽  
Complex Structure ◽  
Complex Structures ◽  
Almost Complex Structure ◽  
Almost Complex Structures ◽  
Almost Complex ◽  
Harmonic Section

Every Walker [Formula: see text]-manifold [Formula: see text], endowed with a canonical neutral metric [Formula: see text], admits a specific almost complex structure called proper. In this paper, we find the conditions under which a proper almost complex structure is a harmonic section or a harmonic map from [Formula: see text] to its hyperbolic twistor space.

scholarly journals A new class of almost complex structures on tangent bundle of a Riemannian manifold

2018 ◽  
Vol 26 (2) ◽  
pp. 137-145
Author(s):  
Amir Baghban ◽  
Esmaeil Abedi
Keyword(s):  
Riemannian Manifold ◽  
Tangent Bundle ◽  
Integrability Condition ◽  
Complex Structure ◽  
Riemannian Metric ◽  
Curvature Operator ◽  
Complex Structures ◽  
New Class ◽  
Almost Complex Structures ◽  
Almost Complex

AbstractIn this paper, the standard almost complex structure on the tangent bunle of a Riemannian manifold will be generalized. We will generalize the standard one to the new ones such that the induced (0, 2)-tensor on the tangent bundle using these structures and Liouville 1-form will be a Riemannian metric. Moreover, under the integrability condition, the curvature operator of the base manifold will be classified.

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