V. Compatible Almost Complex Structures

2006 ◽  
pp. 67-82
Author(s):  
Ana Cannas da Silva
Keyword(s):  
Complex Structures ◽  
Almost Complex Structures ◽  
Almost Complex

scholarly journals Nonexistence of almost complex structures on the product S2m×M

2016 ◽  
Vol 199 ◽  
pp. 102-110 ◽  
Author(s):  
Prateep Chakraborty ◽  
Ajay Singh Thakur
Keyword(s):  
Complex Structures ◽  
Almost Complex Structures ◽  
Almost Complex

scholarly journals Families of(1,2)-symplectic metrics on full flag manifolds

2002 ◽  
Vol 29 (11) ◽  
pp. 651-664 ◽  
Author(s):  
Marlio Paredes
Keyword(s):  
Flag Manifolds ◽  
Invariant Metrics ◽  
Complex Structures ◽  
Symplectic Invariant ◽  
Almost Complex Structures ◽  
Almost Complex ◽  
Complex Flag ◽  
Complex Flag Manifolds

We obtain new families of(1,2)-symplectic invariant metrics on the full complex flag manifoldsF(n). Forn≥5, we characterizen−3differentn-dimensional families of(1,2)-symplectic invariant metrics onF(n). Each of these families corresponds to a different class of nonintegrable invariant almost complex structures onF(n).

A New Class of Almost Complex Structures

2001 ◽  
pp. 602-618
Author(s):  
CHUAN-CHIH HSIUNG ◽  
BONNIE XIONG
Keyword(s):  
Complex Structures ◽  
New Class ◽  
Almost Complex Structures ◽  
Almost Complex

scholarly journals BRANCHED SHADOWS AND COMPLEX STRUCTURES ON 4-MANIFOLDS

2008 ◽  
Vol 17 (11) ◽  
pp. 1429-1454 ◽  
Author(s):  
FRANCESCO COSTANTINO
Keyword(s):  
Complex Structure ◽  
Complex Structures ◽  
Almost Complex Structure ◽  
Homotopy Classes ◽  
Almost Complex Structures ◽  
Almost Complex

We define and study branched shadows of 4-manifolds as a combination of branched spines of 3-manifolds and of Turaev's shadows. We use these objects to combinatorially represent 4-manifolds equipped with Spinc-structures and homotopy classes of almost complex structures. We then use branched shadows to study complex 4-manifolds and prove that each almost complex structure on a 4-dimensional handlebody is homotopic to a complex one.

scholarly journals RELATIVE RUAN AND GROMOV–TAUBES INVARIANTS OF SYMPLECTIC 4-MANIFOLDS

2013 ◽  
Vol 15 (01) ◽  
pp. 1250062
Author(s):  
JOSEF G. DORFMEISTER ◽  
TIAN-JUN LI
Keyword(s):  
Complex Structures ◽  
Almost Complex Structures ◽  
Almost Complex

We define relative Ruan invariants that count embedded connected symplectic submanifolds which contact a fixed symplectic hypersurface V in a symplectic 4-manifold (X, ω) at prescribed points with prescribed contact orders (in addition to insertions on X\V). We obtain invariants of the deformation class of (X, V, ω). Two large issues must be tackled to define such invariants: (1) curves lying in the hypersurface V and (2) genericity results for almost complex structures constrained to make V pseudo-holomorphic (or almost complex). Moreover, these invariants are refined to take into account rim-tori decompositions. In the latter part of the paper, we extend the definition to disconnected submanifolds and construct relative Gromov–Taubes invariants.

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