126
F. Barbaresco
100. Shima, H.: Harmonicity of gradient mappings of level surfaces in a real affine space.
Geometriae Dedicata, pp. 177–184 (1995)
101. Shima, H.: Hessian manifolds of constant Hessian sectional curvature. J. Math. Soc. Japan,
735–753 (1995)
102. Shima, H.: Homogeneous spaces with invariant projectively flat affine connections. Trans.
Am. Math. Soc. 4713–4726 (1999)
103. Shima, H.: The Geometry of Hessian Structures. World Scientific (2007)
104. Shima, H.: Geometry of Hessian Structures, Springer Lecture Notes in Computer Science, Vol.
8085, F. Nielsen, Barbaresco, Frederic (Eds.), pp. 37–55 (2013) (planches: https://www.see.
asso.fr/file/5104/download/25050); (vidéos GSI’13: https://www.youtube.com/watch?time_c
ontinue=139&v=6pyXxdIzDNQ, https://www.youtube.com/watch?time_continue=182&v=
jG2tUjniOUs, https://www.youtube.com/watch?time_continue=6&v=I5kdMJvuNHA)
105. Chu, B.Y.: Symplectic homogeneous spaces. Trans. Am. Math. Soc. 197, 14–159 (1974)
106. Sternberg, S.: Symplectic homogeneous spaces. Trans. Am. Math. Soc. 212, 113–130 (1975)
107. Barbaresco, F.: Lie Group machine learning and gibbs density on poincaré unit disk from
Souriau Lie groups thermodynamics and SU(1,1) coadjoint orbits. In: Nielsen, F., Barbaresco,
F. (eds.) GSI 2019. LNCS, vol. 11712. Springer (2019)
108. Goze, M., Remm, E.: Coadjoint Orbits of Lie Algebras and Cartan Class, Symmetry,
Integrability and Geometry: Methods and Applications, SIGMA 15 (2019)
109. Björn Villa, P.: Kählerian structures of coadjoint orbits of semisimple Lie groups and their orbihedra, Dissertation zur Erlangung des Doktorgrades der Naturwissenschaften an der Fakultät
für Mathematik der Ruhr-Universität Bochum, Jan. (2015)
110. Barbaresco, F.: Jean-Louis Koszul and the Elementary Structures of Information Geometry,
Geometric Structures of Information, pp. 333–392. Springer, Nov. (2018)
111. Koszul, J.L.: Introduction to Symplectic Geometry. Science Press, Beijing (1986) (in chinese);
translated by SPRINGER, with F.Barbaresco, C.M. Marle and M. Boyom forewords,
SPRINGER, 2019
112. Barbaresco, F., Gay-Balmaz, F.: Lie group cohomology and (Multi)symplectic integrators:
new geometric tools for lie group machine learning based on Souriau geometric statistical
mechanics. Entropy 22, 498 (2020)
113. Barbaresco, F.: Lie Group Statistics and Lie Group Machine Learning based on Souriau
Lie Groups Thermodynamics & Koszul-Souriau-Fisher Metric: New Entropy Definition as
Generalized Casimir Invariant Function in Coadjoint Representation, MDPI Entropy (2020)
114. Barbaresco, F.: Radar Processing based on Matrix Lie Groups Geometry & Souriau Coadjoint
Orbits Method, Preprint Academia (2020)
115. Barbaresco, F., Cellodoni, E., Gay-Balmaz, F., Bensoam, J.: Special Issue MDPI Entropy
“Lie Group Machine Learning and Lie Group Structure Preserving Integrators”. https://www.
mdpi.com/journal/entropy/special_issues/Lie_group
116. Les Houches Summer Week, Joint Structures and Common Foundation of Statistical Physics,
Information Geometry and Inference for Learning (SPIGL’20); 26th July to 31st July 2020.
https://franknielsen.github.io/SPIG-LesHouches2020/
117. Tojo, K., Yoshino, T.: On a method to construct exponential families by representation theory.
In: Nielsen, F., Barbaresco, F. (eds.) GSI 2019. LNCS, vol. 11712, Springer (2019)
118. Tojo, K., Yoshino, T.: A method to construct exponential families by representation theory.
arXiv:1811.01394v3
119. Cishahayo, C., De Bièvre, S.: On the contraction of the discrete series of SU(1,1). Ann. Inst.
Fourier 43, 551–567 (1993). https://doi.org/10.5802/aif.1346
120. Cahen, B.: Contraction de SU(1,1) vers le Groupe de Heisenberg, pp. 19–43. Université de
Metz, Fascicule XV, Travaux Mathématiques (2004)
121. Marle, C.-M., Projection stéréographique et moments, hal-02157930, version 1, Juin 2019
122. Adhumeau, T.: Julien Koszul – Correspondances, Les Cahiers BoËllmann-Gigout, 2005
123. Rothaus O. S., The Construction of Homogeneous Convex Cones, Annals of Mathematics,
Ser.2, Vol.83, pp. 358-376, 1966
124. Koszul, J.L.: Formes hermitiennes canoniques des espaces homogènes complexes, Séminaire
Bourbaki, Tome 3, Exposé no. 108, pp. 69–75 (1954–1956)
F. Barbaresco
100. Shima, H.: Harmonicity of gradient mappings of level surfaces in a real affine space.
Geometriae Dedicata, pp. 177–184 (1995)
101. Shima, H.: Hessian manifolds of constant Hessian sectional curvature. J. Math. Soc. Japan,
735–753 (1995)
102. Shima, H.: Homogeneous spaces with invariant projectively flat affine connections. Trans.
Am. Math. Soc. 4713–4726 (1999)
103. Shima, H.: The Geometry of Hessian Structures. World Scientific (2007)
104. Shima, H.: Geometry of Hessian Structures, Springer Lecture Notes in Computer Science, Vol.
8085, F. Nielsen, Barbaresco, Frederic (Eds.), pp. 37–55 (2013) (planches: https://www.see.
asso.fr/file/5104/download/25050); (vidéos GSI’13: https://www.youtube.com/watch?time_c
ontinue=139&v=6pyXxdIzDNQ, https://www.youtube.com/watch?time_continue=182&v=
jG2tUjniOUs, https://www.youtube.com/watch?time_continue=6&v=I5kdMJvuNHA)
105. Chu, B.Y.: Symplectic homogeneous spaces. Trans. Am. Math. Soc. 197, 14–159 (1974)
106. Sternberg, S.: Symplectic homogeneous spaces. Trans. Am. Math. Soc. 212, 113–130 (1975)
107. Barbaresco, F.: Lie Group machine learning and gibbs density on poincaré unit disk from
Souriau Lie groups thermodynamics and SU(1,1) coadjoint orbits. In: Nielsen, F., Barbaresco,
F. (eds.) GSI 2019. LNCS, vol. 11712. Springer (2019)
108. Goze, M., Remm, E.: Coadjoint Orbits of Lie Algebras and Cartan Class, Symmetry,
Integrability and Geometry: Methods and Applications, SIGMA 15 (2019)
109. Björn Villa, P.: Kählerian structures of coadjoint orbits of semisimple Lie groups and their orbihedra, Dissertation zur Erlangung des Doktorgrades der Naturwissenschaften an der Fakultät
für Mathematik der Ruhr-Universität Bochum, Jan. (2015)
110. Barbaresco, F.: Jean-Louis Koszul and the Elementary Structures of Information Geometry,
Geometric Structures of Information, pp. 333–392. Springer, Nov. (2018)
111. Koszul, J.L.: Introduction to Symplectic Geometry. Science Press, Beijing (1986) (in chinese);
translated by SPRINGER, with F.Barbaresco, C.M. Marle and M. Boyom forewords,
SPRINGER, 2019
112. Barbaresco, F., Gay-Balmaz, F.: Lie group cohomology and (Multi)symplectic integrators:
new geometric tools for lie group machine learning based on Souriau geometric statistical
mechanics. Entropy 22, 498 (2020)
113. Barbaresco, F.: Lie Group Statistics and Lie Group Machine Learning based on Souriau
Lie Groups Thermodynamics & Koszul-Souriau-Fisher Metric: New Entropy Definition as
Generalized Casimir Invariant Function in Coadjoint Representation, MDPI Entropy (2020)
114. Barbaresco, F.: Radar Processing based on Matrix Lie Groups Geometry & Souriau Coadjoint
Orbits Method, Preprint Academia (2020)
115. Barbaresco, F., Cellodoni, E., Gay-Balmaz, F., Bensoam, J.: Special Issue MDPI Entropy
“Lie Group Machine Learning and Lie Group Structure Preserving Integrators”. https://www.
mdpi.com/journal/entropy/special_issues/Lie_group
116. Les Houches Summer Week, Joint Structures and Common Foundation of Statistical Physics,
Information Geometry and Inference for Learning (SPIGL’20); 26th July to 31st July 2020.
https://franknielsen.github.io/SPIG-LesHouches2020/
117. Tojo, K., Yoshino, T.: On a method to construct exponential families by representation theory.
In: Nielsen, F., Barbaresco, F. (eds.) GSI 2019. LNCS, vol. 11712, Springer (2019)
118. Tojo, K., Yoshino, T.: A method to construct exponential families by representation theory.
arXiv:1811.01394v3
119. Cishahayo, C., De Bièvre, S.: On the contraction of the discrete series of SU(1,1). Ann. Inst.
Fourier 43, 551–567 (1993). https://doi.org/10.5802/aif.1346
120. Cahen, B.: Contraction de SU(1,1) vers le Groupe de Heisenberg, pp. 19–43. Université de
Metz, Fascicule XV, Travaux Mathématiques (2004)
121. Marle, C.-M., Projection stéréographique et moments, hal-02157930, version 1, Juin 2019
122. Adhumeau, T.: Julien Koszul – Correspondances, Les Cahiers BoËllmann-Gigout, 2005
123. Rothaus O. S., The Construction of Homogeneous Convex Cones, Annals of Mathematics,
Ser.2, Vol.83, pp. 358-376, 1966
124. Koszul, J.L.: Formes hermitiennes canoniques des espaces homogènes complexes, Séminaire
Bourbaki, Tome 3, Exposé no. 108, pp. 69–75 (1954–1956)