Abstract
Abstract
Given the Frölicher-Nijenhuis bicomplex
(
d
,
d
L
)
associated with a
(
1
,
1
)
-tensor field L with vanishing Nijenhuis torsion, we define a multi-parameter family of bi-flat structures
(
∇
,
e
,
∘
,
∇
∗
,
∗
,
E
)
. This result is obtained by combining the construction of integrable hierarchies of hydrodynamic type starting from Frölicher-Nijenhuis bicomplexes with the construction of flat F-manifold structures from integrable systems of hydrodynamic type. By construction L is the operator of multiplication by the Euler vector field E and the number of parameters coincides with the number of Jordan blocks appearing in its Jordan normal form. We call these structures Lauricella bi-flat structures since in the n-dimensional semisimple case
(
n
−
1
)
flat coordinates of
∇
are Lauricella functions. The
(
1
,
1
)
-tensor fields defining the corresponding integrable hierarchies have a similar block diagonal structure.
Funder
H2020 Marie Skłodowska-Curie Actions
Subject
Applied Mathematics,General Physics and Astronomy,Mathematical Physics,Statistical and Nonlinear Physics
Cited by
1 articles.
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