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Journal articles on the topic 'Application holomorphe'

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Published: 4 June 2021

Last updated: 4 May 2024

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1

Gruman, Lawrence. "L'image d'une application holomorphe." Annales de la faculté des sciences de Toulouse Mathématiques 12, no. 1 (1991): 75–101. http://dx.doi.org/10.5802/afst.720.

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2

Mazet, Pierre, and Jean-Pierre Vigué. "Points fixes d'une application holomorphe d'un domaine borné dans lui-même." Acta Mathematica 166 (1991): 1–26. http://dx.doi.org/10.1007/bf02398882.

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3

Abd-Alla, Mohamed. "L'ensemble des points fixes d'une application holomorphe dans un produit fini de boules-unités d'espaces de Hilbert est une sous-variété banachique complexe." Annali di Matematica Pura ed Applicata (1923 -) 153, no. 1 (1988): 63–75. http://dx.doi.org/10.1007/bf01762386.

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4

Pavlovsky, Vladislav A., and Igor L. Vasiliev. "On properties of h-differentiable functions." Journal of the Belarusian State University. Mathematics and Informatics, no. 2 (August 5, 2021): 29–37. http://dx.doi.org/10.33581/2520-6508-2021-2-29-37.

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Research in the theory of functions of an h-complex variable is of interest in connection with existing applications in non-Euclidean geometry, theoretical mechanics, etc. This article is devoted to the study of the properties of h-differentiable functions. Criteria for h-differentiability and h-holomorphy are found, formulated and proved a theorem on finite increments for an h-holomorphic function. Sufficient conditions for h-analyticity are given, formulated and proved a uniqueness theorem for h-analytic functions.

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5

Kim, Henry H. "On Local L-Functions and Normalized Intertwining Operators." Canadian Journal of Mathematics 57, no. 3 (2005): 535–97. http://dx.doi.org/10.4153/cjm-2005-023-x.

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AbstractIn this paper we make explicit all L-functions in the Langlands–Shahidi method which appear as normalizing factors of global intertwining operators in the constant term of the Eisenstein series. We prove, in many cases, the conjecture of Shahidi regarding the holomorphy of the local L-functions. We also prove that the normalized local intertwining operators are holomorphic and non-vaninishing for Re(s) ≥ 1/2 in many cases. These local results are essential in global applications such as Langlands functoriality, residual spectrumand determining poles of automorphic L-functions.

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6

Damour, Sylvain. "Sur l'algébricité des applications holomorphes." Comptes Rendus de l'Académie des Sciences - Series I - Mathematics 332, no. 6 (2001): 491–96. http://dx.doi.org/10.1016/s0764-4442(01)01887-0.

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7

Maingot, Stéphane. "Multitype et applications holomorphes propres." Mathematische Zeitschrift 208, no. 1 (1991): 617–26. http://dx.doi.org/10.1007/bf02571549.

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8

Kosiek, Marek, and Krzysztof Rudol. "Dual Algebras and A-Measures." Journal of Function Spaces 2014 (2014): 1–8. http://dx.doi.org/10.1155/2014/364271.

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Weak-star closures of Gleason parts in the spectrum of a function algebra are studied. These closures relate to the bidual algebra and turn out both closed and open subsets of a compact hyperstonean space. Moreover, weak-star closures of the corresponding bands of measures are reducing. Among the applications we have a complete solution of an abstract version of the problem, whether the set of nonnegative A-measures (called also Henkin measures) is closed with respect to the absolute continuity. When applied to the classical case of analytic functions on a domain of holomorphyΩ⊂Cn, our approac

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9

Cerveau, D. "Un lemme de prolongement holomorphe et ses applications." Bulletin des Sciences Mathématiques 127, no. 3 (2003): 215–21. http://dx.doi.org/10.1016/s0007-4497(03)00008-3.

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10

Chinea, Domingo. "Harmonicity of Holomorphic Maps Between Almost Hermitian Manifolds." Canadian Mathematical Bulletin 52, no. 1 (2009): 18–27. http://dx.doi.org/10.4153/cmb-2009-003-4.

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AbstractIn this paper we study holomorphic maps between almost Hermitian manifolds. We obtain a new criterion for the harmonicity of such holomorphic maps, and we deduce some applications to horizontally conformal holomorphic submersions.

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11

Dupré, Maurice J., and James F. Glazebrook. "Holomorphic Framings for Projections in A Banach Algebra." gmj 9, no. 3 (2002): 481–94. http://dx.doi.org/10.1515/gmj.2002.481.

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Abstract Given a complex Banach algebra, we consider the Stiefel bundle relative to the similarity class of a fixed projection. In the holomorphic category the Stiefel bundle is a holomorphic locally trivial principal bundle over a certain Grassmann manifold. Our main application concerns the holomorphic parametrization of framings for projections. In the spatial case this amounts to a holomorphic parametrization of framings for a corresponding complex Banach space.

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12

Chan, Shan Tai, Ming Xiao, and Yuan Yuan. "Holomorphic isometries between products of complex unit balls." International Journal of Mathematics 28, no. 09 (2017): 1740010. http://dx.doi.org/10.1142/s0129167x17400109.

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We first give an exposition on holomorphic isometries from the Poincaré disk to polydisks and from the Poincaré disk to the product of the Poincaré disk with a complex unit ball. As an application, we provide an example of proper holomorphic map from the unit disk to the complex unit ball that is irrational, algebraic and holomorphic on a neighborhood of the closed unit disk. We also include some new results on holomorphic isometries.

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13

Lindström, Mikael, and R. A. Ryan. "Applications of Ultraproducts to Infinite Dimensional Holomorphy." MATHEMATICA SCANDINAVICA 71 (June 1, 1992): 229. http://dx.doi.org/10.7146/math.scand.a-12424.

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14

Loeb, J. J. "Applications holomorphes de domaines disqués non bornés." Publicacions Matemàtiques 50 (January 1, 2006): 149–65. http://dx.doi.org/10.5565/publmat_50106_08.

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15

Coupet, Bernard, Yifei Pan, and Alexandre Sukhov. "On proper holomorphic mappings from domains with T-action." Nagoya Mathematical Journal 154 (1999): 57–72. http://dx.doi.org/10.1017/s0027763000025307.

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AbstractWe describe the branch locus of a proper holomorphic mapping between two smoothly bounded pseudoconvex domains of finite type in under the assumption that the first domain admits a transversal holomorphic action of the unit circle. As an application we show that any proper holomorphic self-mapping of a smoothly bounded pseudoconvex complete circular domain of finite type in is biholomorphic.

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16

Mazet, Pierre. "Principe du Maximum et Lemme de Schwarz a Valeurs Vectorielles." Canadian Mathematical Bulletin 40, no. 3 (1997): 356–63. http://dx.doi.org/10.4153/cmb-1997-042-9.

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RésuméNous établissons un théorème pour les fonctions holomorphes à valeurs dans une partie convexe fermée. Ce théorème précise la position des coefficients de Taylor de telles fonctions et peut être considéré comme une généralisation des inégalités de Cauchy. Nous montrons alors comment ce théorème permet de retrouver des versions connues du principe du maximum et d’obtenir de nouveaux résultats sur les applications holomorphes à valeurs vectorielles.

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17

GAO, YANG, and BAI-XIANG XU. "METHOD ON HOLOMORPHIC VECTOR FUNCTIONS AND APPLICATIONS IN TWO-DIMENSIONAL QUASICRYSTALS." International Journal of Modern Physics B 22, no. 06 (2008): 635–43. http://dx.doi.org/10.1142/s021797920803882x.

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Generalization of the Stroh formalism to two-dimensional quasicrystal materials results in a ten-dimensional formalism for which there are five pairs of complex eigenvalues. By virtue of the generalized Stroh formalism, two-dimensional problems of quasicrystals elasticity are transferred into the boundary value problems of holomorphic vector functions in a given region. If the conformal mapping from an ellipse to a circle is known, a general method can be presented for solving the boundary value problems of holomorphic vector functions. Using the necessary and sufficient condition of boundary

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18

XIAO, JINXIU, CHUNHUI QIU, QUN HE, and ZHIHUA CHEN. "LAPLACIAN COMPARISON ON COMPLEX FINSLER MANIFOLDS AND ITS APPLICATIONS." International Journal of Mathematics 24, no. 05 (2013): 1350034. http://dx.doi.org/10.1142/s0129167x13500341.

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By defining the Rund Laplacian, we obtain the first and the second holomorphic variation formulas for the strongly pseudoconvex complex Finsler metric. Using the holomorphic variation formulas, we get an estimate for the Levi forms of distance function on complex Finsler manifolds. Further, an estimate for the Rund Laplacians of distance function on strongly pseudoconvex complex Finsler manifolds is obtained. As its applications, we get the Bonnet theorem and maximum principle on complex Finsler manifolds.

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19

Charles, François, Giovanni Mongardi, and Gianluca Pacienza. "Families of rational curves on holomorphic symplectic varieties and applications to 0-cycles." Compositio Mathematica 160, no. 2 (2023): 288–316. http://dx.doi.org/10.1112/s0010437x20007526.

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We study families of rational curves on irreducible holomorphic symplectic varieties. We give a necessary and sufficient condition for a sufficiently ample linear system on a holomorphic symplectic variety of $K3^{[n]}$ -type to contain a uniruled divisor covered by rational curves of primitive class. In particular, for any fixed $n$ , we show that there are only finitely many polarization types of holomorphic symplectic variety of $K3^{[n]}$ -type that do not contain such a uniruled divisor. As an application, we provide a generalization of a result due to Beauville–Voisin on the Chow group o

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20

Kim, Henry H. "Langlands-Shahidi Method and Poles of Automorphic L-Functions: Application to Exterior Square L-Functions." Canadian Journal of Mathematics 51, no. 4 (1999): 835–49. http://dx.doi.org/10.4153/cjm-1999-036-0.

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AbstractIn this paper we use Langlands-Shahidimethod and the result of Langlands which says that non selfconjugatemaximal parabolic subgroups do not contribute to the residual spectrum, to prove the holomorphy of several completed automorphic L-functions on the whole complex plane which appear in constant terms of the Eisenstein series. They include the exterior square L-functions of GLn, n odd, the Rankin-Selberg L-functions of GLn × GLm, n ≠ m, and L-functions L(s, σ, r), where σ is a generic cuspidal representation of SO10 and r is the half-spin representation of GSpin(10, ). The main part

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21

RONG, FENG, and BEN ZHANG. "HOLOMORPHIC AUTOMORPHISMS AND PROPER HOLOMORPHIC SELF-MAPPINGS OF A TYPE OF GENERALISED MINIMAL BALL." Bulletin of the Australian Mathematical Society 96, no. 3 (2017): 455–67. http://dx.doi.org/10.1017/s0004972717000545.

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In this paper, we first give a description of the holomorphic automorphism group of a convex domain which is a simple case of the so-called generalised minimal ball. As an application, we show that any proper holomorphic self-mapping on this type of domain is biholomorphic.

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22

Jiang, Yunping, and Sudeb Mitra. "Some applications of universal holomorphic motions." Kodai Mathematical Journal 30, no. 1 (2007): 85–96. http://dx.doi.org/10.2996/kmj/1175287624.

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23

Pinchuk, S. I., and S. V. Khasanov. "ASYMPTOTICALLY HOLOMORPHIC FUNCTIONS AND THEIR APPLICATIONS." Mathematics of the USSR-Sbornik 62, no. 2 (1989): 541–50. http://dx.doi.org/10.1070/sm1989v062n02abeh003253.

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24

Kim, Henry H., Satoshi Wakatsuki, and Takuya Yamauchi. "AN EQUIDISTRIBUTION THEOREM FOR HOLOMORPHIC SIEGEL MODULAR FORMS FOR AND ITS APPLICATIONS." Journal of the Institute of Mathematics of Jussieu 19, no. 2 (2018): 351–419. http://dx.doi.org/10.1017/s147474801800004x.

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We prove an equidistribution theorem for a family of holomorphic Siegel cusp forms for $\mathit{GSp}_{4}/\mathbb{Q}$ in various aspects. A main tool is Arthur’s invariant trace formula. While Shin [Automorphic Plancherel density theorem, Israel J. Math.192(1) (2012), 83–120] and Shin–Templier [Sato–Tate theorem for families and low-lying zeros of automorphic $L$-functions, Invent. Math.203(1) (2016) 1–177] used Euler–Poincaré functions at infinity in the formula, we use a pseudo-coefficient of a holomorphic discrete series to extract holomorphic Siegel cusp forms. Then the non-semisimple contr

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25

Van Nguyen, Thanh, and Ahmed Zeriahi. "Systèmes doublement orthogonaux de fonctions holomorphes et applications." Banach Center Publications 31, no. 1 (1995): 281–97. http://dx.doi.org/10.4064/-31-1-281-297.

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26

Risler, Emmanuel. "Linéarisation des perturbations holomorphes des rotations et applications." Mémoires de la Société mathématique de France 1 (1999): 1–102. http://dx.doi.org/10.24033/msmf.390.

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27

Asserda, Said, and M'hamed Kassi. "Courants de type Liouville pour les applications holomorphes." Comptes Rendus Mathematique 335, no. 9 (2002): 751–56. http://dx.doi.org/10.1016/s1631-073x(02)02558-x.

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28

Blanc-Centi, Léa. "Régularité au bord des applications pseudo-holomorphes propres." Comptes Rendus Mathematique 345, no. 8 (2007): 421–24. http://dx.doi.org/10.1016/j.crma.2007.09.013.

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29

PAN, Lishuang, and An WANG. "Application of holomorphic invariants in reproducing kernel." Acta Mathematica Scientia 37, no. 2 (2017): 355–67. http://dx.doi.org/10.1016/s0252-9602(17)30007-3.

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30

Belomestny, Denis, Jörg Kampen, and John Schoenmakers. "Holomorphic transforms with application to affine processes." Journal of Functional Analysis 257, no. 4 (2009): 1222–50. http://dx.doi.org/10.1016/j.jfa.2009.03.013.

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31

KAZAMA, Hideaki, and Takashi UMENO. "Dolbeault isomorphisms for holomorphic vector bundles over holomorphic fiber spaces and applications." Journal of the Mathematical Society of Japan 45, no. 1 (1993): 121–30. http://dx.doi.org/10.2969/jmsj/04510121.

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32

Shen, Yuliang. "The asymptotic Teichmüller space and the asymptotic Grunsky map." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 140, no. 3 (2010): 651–72. http://dx.doi.org/10.1017/s0308210509000560.

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The Grunsky map is known to be holomorphic on the universal Teichmüller space. In this paper it is proved that the Grunsky map induces a holomorphic map on the asymptotic Teichmüller space. The Caratháodory and Kobayashi metrics on the asymptotic Teichmüller space are studied as applications.

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33

STOPAR, KRIS. "APPROXIMATION OF HOLOMORPHIC MAPPINGS ON 1-CONVEX DOMAINS." International Journal of Mathematics 24, no. 14 (2013): 1350108. http://dx.doi.org/10.1142/s0129167x13501085.

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Let π : Z → X be a holomorphic submersion of a complex manifold Z onto a complex manifold X and D ⋐ X a 1-convex domain with strongly pseudoconvex boundary. We prove that under certain conditions there always exists a spray of π-sections over [Formula: see text] which has prescribed core, it fixes the exceptional set E of D, and is dominating on [Formula: see text]. Each section in this spray is of class [Formula: see text] and holomorphic on D. As a consequence we obtain several approximation results for π-sections. In particular, we prove that π-sections which are of class [Formula: see text

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34

Bruzzo, Ugo, Igor Mencattini, Vladimir N. Rubtsov, and Pietro Tortella. "Nonabelian holomorphic Lie algebroid extensions." International Journal of Mathematics 26, no. 05 (2015): 1550040. http://dx.doi.org/10.1142/s0129167x15500408.

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We classify nonabelian extensions of Lie algebroids in the holomorphic category. Moreover we study a spectral sequence associated to any such extension. This spectral sequence generalizes the Hochschild–Serre spectral sequence for Lie algebras to the holomorphic Lie algebroid setting. As an application, we show that the hypercohomology of the Atiyah algebroid of a line bundle has a natural Hodge structure.

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35

BOROT, GAËTAN, and SERGEY SHADRIN. "Blobbed topological recursion: properties and applications." Mathematical Proceedings of the Cambridge Philosophical Society 162, no. 1 (2016): 39–87. http://dx.doi.org/10.1017/s0305004116000323.

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AbstractWe study the set of solutions (ωg,n)g⩾0,n⩾1 of abstract loop equations. We prove that ωg,n is determined by its purely holomorphic part: this results in a decomposition that we call “blobbed topological recursion”. This is a generalisation of the theory of the topological recursion, in which the initial data (ω0,1, ω0,2) is enriched by non-zero symmetric holomorphic forms in n variables (φg,n)2g−2+n>0. In particular, we establish for any solution of abstract loop equations: (1) a graphical representation of ωg,n in terms of φg,n; (2) a graphical representation of ωg,n in terms of in

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36

Choi, SoYoung, and Chang Heon Kim. "Explicit construction of mock modular forms from weakly holomorphic Hecke eigenforms." Open Mathematics 20, no. 1 (2022): 313–32. http://dx.doi.org/10.1515/math-2022-0009.

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Abstract Extending our previous work we construct weakly holomorphic Hecke eigenforms whose period polynomials correspond to elements in a basis consisting of odd and even Hecke eigenpolynomials induced by only cusp forms. As an application of our results, we give an explicit construction of the holomorphic parts of harmonic weak Maass forms that are good for Hecke eigenforms. Moreover, we give an explicit construction of the Hecke-equivariant map between the space of weakly holomorphic cusp forms and two copies of the spaces of cusp forms, and show that the map is compatible with the correspo

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37

BERMAN, ROBERT J. "BERGMAN KERNELS AND EQUILIBRIUM MEASURES FOR POLARIZED PSEUDO-CONCAVE DOMAINS." International Journal of Mathematics 21, no. 01 (2010): 77–115. http://dx.doi.org/10.1142/s0129167x10005933.

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Let X be a domain in a closed polarized complex manifold (Y,L), where L is a (semi-) positive line bundle over Y. Any given Hermitian metric on L induces by restriction to X a Hilbert space structure on the space of global holomorphic sections on Y with values in the k-th tensor power of L (also using a volume form ωn on X. In this paper the leading large k asymptotics for the corresponding Bergman kernels and metrics are obtained in the case when X is a pseudo-concave domain with smooth boundary (under a certain compatibility assumption). The asymptotics are expressed in terms of the curvatur

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38

Eum, Ick Sun, Ja Kyung Koo, and Dong Hwa Shin. "Some applications of modular units." Proceedings of the Edinburgh Mathematical Society 59, no. 1 (2015): 91–106. http://dx.doi.org/10.1017/s0013091514000352.

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AbstractWe show that a weakly holomorphic modular function can be written as a sum of modular units of higher level. Furthermore, we find a necessary and sufficient condition for a meromorphic Siegel modular function of degree g to have neither a zero nor a pole on a certain subset of the Siegel upper half-space .

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39

Ni, Lei. "General Schwarz Lemmata and their applications." International Journal of Mathematics 30, no. 13 (2019): 1940007. http://dx.doi.org/10.1142/s0129167x1940007x.

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We prove estimates interpolating the Schwarz Lemmata of Royden–Yau and the ones recently established by the author. These more flexible estimates provide additional information on (algebraic) geometric aspects of compact Kähler manifolds with nonnegative holomorphic sectional curvature, nonnegative [Formula: see text] or positive [Formula: see text].

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40

Pavićević, Žarko, and Valerian Ivanovich Gavrilov. "Boundary characteristics of meromorphic functions with summable spherical derivation and annular functions. Consideration." Mathematica Montisnigri 51 (August 2021): 5–17. http://dx.doi.org/10.20948/mathmontis-2021-51-1.

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In this paper we formulate classical theorems Plesner and Meyer on the boundary behavior of meromorphic functions and their refinement and strengthening - Gavrilov's and Kanatnikov's theorems. An application of these theorems to classes of meromorphic functions with integrable spherical derivative and annular holomorphic functions is presented. Collingwood's theorem on boundary singularities of the Tsuji function as well as Kanatnikov's theorems are formulated. Kanatnikov's theorems strengthen and generalize Collingwood's theorem to broader classes of meromorphic functions with summable spheri

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41

Kassabov, Ognian, and Velichka Milousheva. "Minimal timelike surfaces in the Lorentz–Minkowski 3-space and their canonical parameters." Serdica Mathematical Journal 49, no. 4 (2024): 301–16. http://dx.doi.org/10.55630/serdica.2023.49.301-316.

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We study minimal timelike surfaces in \(\mathbb R^3_1\) using a special Weierstrass-type formula in terms of holomorphic functions defined in the algebra of the double (split-complex) numbers. We present a method of obtaining an equation of a minimal timelike surface in terms of canonical parameters, which play a role similar to the role of the natural parameters of curves in \(\mathbb R^3\). Having one holomorphic function that generates a minimal timelike surface, we find all holomorphic functions that generate the same surface. In this way we give a correspondence between a minimal timelike

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42

Kusakabe, Yuta. "Dense holomorphic curves in spaces of holomorphic maps and applications to universal maps." International Journal of Mathematics 28, no. 04 (2017): 1750028. http://dx.doi.org/10.1142/s0129167x17500288.

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We study when there exists a dense holomorphic curve in a space of holomorphic maps from a Stein space. We first show that for any bounded convex domain [Formula: see text] and any connected complex manifold [Formula: see text], the space [Formula: see text] contains a dense holomorphic disc. Our second result states that [Formula: see text] is an Oka manifold if and only if for any Stein space [Formula: see text] there exists a dense entire curve in every path component of [Formula: see text]. In the second half of this paper, we apply the above results to the theory of universal functions. I

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43

Ourimi, Nabil. "Applications holomorphes propres entre certains domaines bornés de ℂn". Comptes Rendus de l'Académie des Sciences - Series I - Mathematics 326, № 9 (1998): 1063–68. http://dx.doi.org/10.1016/s0764-4442(98)80063-3.

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44

Nishimura, Yasuichiro. "Applications holomorphes injectives à jacobien constant de deux variables." Journal of Mathematics of Kyoto University 26, no. 4 (1986): 697–709. http://dx.doi.org/10.1215/kjm/1250520836.

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45

Dektyarev, I. M. "Multivariable value distribution theory. Application to holomorphic curves." Journal of Mathematical Sciences 92, no. 2 (1998): 3685–711. http://dx.doi.org/10.1007/bf02434004.

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46

Floret, Klaus, and Mário C. Matos. "Application of a Khintchine Inequality to Holomorphic Mappings." Mathematische Nachrichten 176, no. 1 (1995): 65–72. http://dx.doi.org/10.1002/mana.19951760106.

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47

SIDDIQUI, ALIYA NAAZ, and MOHAMMAD HASAN SHAHID. "Optimizations on Statistical Hypersurfaces with Casorati Curvatures." Kragujevac Journal of Mathematics 45, no. 03 (2021): 449–63. http://dx.doi.org/10.46793/kgjmat2103.449s.

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In the present paper, we study Casorati curvatures for statistical hypersurfaces. We show that the normalized scalar curvature for any real hypersurface (i.e., statistical hypersurface) of a holomorphic statistical manifold of constant holomorphic sectional curvature k is bounded above by the generalized normalized δ−Casorati curvatures and also consider the equality case of the inequality. Some immediate applications are discussed.

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48

Seo, Won-Ki. "Fredholm inversion around a singularity: Application to autoregressive time series in Banach space." Electronic Research Archive 31, no. 8 (2023): 4925–50. http://dx.doi.org/10.3934/era.2023252.

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<abstract><p>This paper considers inverting a holomorphic Fredholm operator pencil. Specifically, we provide necessary and sufficient conditions for the inverse of a holomorphic Fredholm operator pencil to have a simple pole and a second order pole. Based on these results, a closed-form expression of the Laurent expansion of the inverse around an isolated singularity is obtained in each case. As an application, we also obtain a suitable extension of the Granger-Johansen representation theorem for random sequences taking values in a separable Banach space. Due to our closed-form exp

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49

Wang, Xiaodong. "An integral formula in Kähler geometry with applications." Communications in Contemporary Mathematics 19, no. 05 (2016): 1650063. http://dx.doi.org/10.1142/s0219199716500632.

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We establish an integral formula on a smooth, precompact domain in a Kähler manifold. We apply this formula to study holomorphic extension of CR functions. Using this formula, we also prove some geometric inequalities when the boundary has positive Hermitian mean curvature.

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50

Biswas, Indranil, Sorin Dumitrescu та Henri Guenancia. "A Bochner principle and its applications to Fujiki class 𝒞 manifolds with vanishing first Chern class". Communications in Contemporary Mathematics 22, № 06 (2019): 1950051. http://dx.doi.org/10.1142/s0219199719500512.

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We prove a Bochner-type vanishing theorem for compact complex manifolds [Formula: see text] in Fujiki class [Formula: see text], with vanishing first Chern class, that admit a cohomology class [Formula: see text] which is numerically effective (nef) and has positive self-intersection (meaning [Formula: see text], where [Formula: see text]). Using it, we prove that all holomorphic geometric structures of affine type on such a manifold [Formula: see text] are locally homogeneous on a non-empty Zariski open subset. Consequently, if the geometric structure is rigid in the sense of Gromov, then the

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