scholarly journals The leaf space of a multiplicative foliation

2012 ◽  
Vol 4 (3) ◽  
pp. 313-332 ◽  
Author(s):  
M. Jotz ◽  
Keyword(s):  
Leaf Space

scholarly journals Riemannian foliations with Ehresmann connection

2018 ◽  
Vol 20 (4) ◽  
pp. 395-407
Author(s):  
N. I. Zhukova
Keyword(s):  
Linear Connection ◽  
Riemannian Foliation ◽  
Minimal Set ◽  
Foliated Manifold ◽  
Trivial Bundle ◽  
Riemannian Foliations ◽  
Ehresmann Connection ◽  
The Family ◽  
Leaf Space ◽  
Complete Riemannian Manifolds

It is shown that the structural theory of Molino for Riemannian foliations on compact manifolds and complete Riemannian manifolds may be generalized to a Riemannian foliations with Ehresmann connection. Within this generalization there are no restrictions on the codimension of the foliation and on the dimension of the foliated manifold. For a Riemannian foliation (M,F) with Ehresmann connection it is proved that the closure of any leaf forms a minimal set, the family of all such closures forms a singular Riemannian foliation (M,F¯¯¯¯). It is shown that in M there exists a connected open dense F¯¯¯¯-saturated subset M0 such that the induced foliation (M0,F¯¯¯¯|M0) is formed by fibers of a locally trivial bundle over some smooth Hausdorff manifold. The equivalence of some properties of Riemannian foliations (M,F) with Ehresmann connection is proved. In particular, it is shown that the structural Lie algebra of (M,F) is equal to zero if and only if the leaf space of (M,F) is naturally endowed with a smooth orbifold structure. Constructed examples show that for foliations with transversally linear connection and for conformal foliations the similar statements are not true in general.

scholarly journals On the de rham cohomology of the leaf space of a foliation

Topology ◽  
1974 ◽  
Vol 13 (2) ◽  
pp. 185-187 ◽  
Author(s):  
Gerald W. Schwarz
Keyword(s):  
De Rham Cohomology ◽  
De Rham ◽  
Leaf Space

Identification of QTL for leaf angle and leaf space above ear position across different environments and generations in maize (Zea mays L.)

Euphytica ◽  
2015 ◽  
Vol 204 (2) ◽  
pp. 395-405 ◽  
Author(s):  
Xining Chen ◽  
De Xu ◽  
Zheng Liu ◽  
Tingting Yu ◽  
Xiupeng Mei ◽  
...  
Keyword(s):  
Zea Mays ◽  
Zea Mays L ◽  
Leaf Angle ◽  
Leaf Space

scholarly journals New relations between G2 geometries in dimensions 5 and 7

2017 ◽  
Vol 28 (13) ◽  
pp. 1750094 ◽  
Author(s):  
Thomas Leistner ◽  
Paweł Nurowski ◽  
Katja Sagerschnig
Keyword(s):  
Contact Structure ◽  
Closed Orbit ◽  
Geometric Construction ◽  
Contact Structures ◽  
Curvature Condition ◽  
Cartan Connections ◽  
Leaf Space

There are two well-known parabolic split [Formula: see text] geometries in dimension 5, [Formula: see text] distributions and [Formula: see text] contact structures. Here we link these two geometries with yet another [Formula: see text] related contact structure, which lives on a [Formula: see text]-manifold. More precisely, we present a natural geometric construction that associates to a [Formula: see text] distribution a [Formula: see text]-dimensional bundle endowed with a canonical Lie contact structure. We further study the relation between the canonical normal Cartan connections associated with the two structures and we show that the Cartan holonomy of the induced Lie contact structure reduces to [Formula: see text]. This motivates the study of the curved orbit decomposition associated with a [Formula: see text] reduced Lie contact structure on a [Formula: see text]-manifold. It is shown that, provided an additional curvature condition is satisfied, in a neighborhood of each point in the open curved orbit the structure descends to a [Formula: see text] distribution on a local leaf space. The closed orbit carries an induced [Formula: see text] contact structure.

Morphological Structure Model of Leaf Space Based on Biomass at Pre-Overwintering Stage in Rapeseed (Brassica napusL.) Plant

2015 ◽  
Vol 41 (2) ◽  
pp. 318 ◽  
Author(s):  
Wei-Xin ZHANG ◽  
Hong-Xin CAO ◽  
Yan ZHU ◽  
Yan LIU ◽  
Wen-Yu ZHANG ◽  
...  
Keyword(s):  
Morphological Structure ◽  
Structure Model ◽  
Leaf Space

scholarly journals ON CLOSED GEODESICS IN THE LEAF SPACE OF SINGULAR RIEMANNIAN FOLIATIONS

2011 ◽  
Vol 53 (3) ◽  
pp. 555-568 ◽  
Author(s):  
MARCOS M. ALEXANDRINO ◽  
MIGUEL ANGEL JAVALOYES
Keyword(s):  
Conjugate Points ◽  
Closed Geodesics ◽  
Riemannian Foliations ◽  
Singular Riemannian Foliations ◽  
Leaf Space

AbstractIn this paper we prove the existence of closed geodesics in the leaf space of some classes of singular Riemannian foliations (s.r.f.), namely s.r.fs. that admit sections or have no horizontal conjugate points. We also investigate the shortening process with respect to Riemannian foliations.

Carbon Fixation Profiles Do Reflect Light Absorption Profiles in Leaves

1995 ◽  
Vol 22 (6) ◽  
pp. 865 ◽  
Author(s):  
JR Evans
Keyword(s):  
Light Absorption ◽  
Carbon Fixation ◽  
Protein Complexes ◽  
Lower Surface ◽  
High Irradiance ◽  
Absorption Profile ◽  
Light Gradient ◽  
Pigment Protein Complexes ◽  
Leaf Space ◽  
Leaf Photosynthetic Rate

Bifacial leaves contain an array of chloroplasts which are aligned along cell walls adjacent to intercellular airspaces. Cells beneath the adaxial (upper) surface are generally cylindrical in shape, forming palisade tissue and contain chloroplasts that have characteristics associated with acclimation to high irradiance. Conversely, cells near the abaxial (lower) surface are irregular in shape, forming spongy tissue and contain chloroplasts that have characteristics associated with acclimation to low irradiance. This results in a gradient of declining photosynthetic capacity per unit chlorophyll with increasing depth into the leaf. Space irradiance declines dramatically through the leaf. The profile of light absorption through the leaf has yet to be measured, but should approximate the product of space irradiance and pigment profiles. Since pigment content is highest in the middle of the leaf, light absorption peaks about one quarter of the way through the leaf. The response of leaf photosynthetic rate to irradiance reflects the interaction between the profiles of light absorption and chloroplast characteristics. Quantum yield (mol CO2 mol-1 quanta absorbed) varies for different layers in the leaf because the profile of Rubisco content per unit chlorophyll is not as steep as the light absorption profile. This skews the profile of carbon fixation away from the light absorption profile, favouring greater fixation in deeper layers. Nishio, Sun and Vogelmann (1993, Plant Cell 5, 953-961) measured profiles of 14C fixation across spinach leaves and concluded that carbon fixation was disconnected from the light gradient. Reanalysis of their data shows that carbon fixation is remarkably consistent with light absorption obeying the Beer- Lambert law when allowance is made for chlorophyll and Rubisco profiles through the leaf. This interpretation is supported by chlorophyll fluorescence properties of adaxial and abaxial surfaces. An apparent extinction coefficient of about 1500 m2 (mol Chl)-1 could be derived from leaf data which compares with 2230 m2 (mol Chl)-1 for pigment-protein complexes in solution. A possible test for this analysis would be to measure the 14C fixation profile of leaves illuminated on their abaxial surface.

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