Year 2020, Volume 49 , Issue 1, Pages 120 - 135 2020-02-06

Statistical structures on the tangent bundle of a statistical manifold with Sasaki metric

Vladimir BALAN [1] , E. PEYGHAN [2] , Esa SHARAHİ [3]


The first part of the paper is devoted to the classification of the statistical structures which live on the tangent bundle of a statistical manifold endowed with a Sasaki metric. Further, considering a Kähler structure on the base statistical manifold, we introduce a family of almost complex structures on the tangent bundle equipped with the Sasaki metric, and find equivalent conditions for which this family induces a Kähler structure. Finally, we derive equivalent conditions for existence of holomorphic structures on the tangent bundle equipped with the Sasaki metric in the presence of a statistical structure. Several illustrative examples are provided, as well.
Holomorphic statistical manifold, statistical structure, Kähler structure, Sasaki metric
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Primary Language en
Subjects Mathematics
Journal Section Mathematics
Authors

Orcid: 0000-0002-0124-4205
Author: Vladimir BALAN
Institution: University Politehnica of Bucharest
Country: Romania


Orcid: 0000-0002-2713-6253
Author: E. PEYGHAN
Institution: Arak University
Country: Iran


Orcid: 0000-0002-1749-7469
Author: Esa SHARAHİ
Institution: Arak University
Country: Iran


Dates

Publication Date : February 6, 2020

Bibtex @research article { hujms535195, journal = {Hacettepe Journal of Mathematics and Statistics}, issn = {2651-477X}, eissn = {2651-477X}, address = {}, publisher = {Hacettepe University}, year = {2020}, volume = {49}, pages = {120 - 135}, doi = {10.15672/HJMS.2019.667}, title = {Statistical structures on the tangent bundle of a statistical manifold with Sasaki metric}, key = {cite}, author = {BALAN, Vladimir and PEYGHAN, E. and SHARAHİ, Esa} }
APA BALAN, V , PEYGHAN, E , SHARAHİ, E . (2020). Statistical structures on the tangent bundle of a statistical manifold with Sasaki metric. Hacettepe Journal of Mathematics and Statistics , 49 (1) , 120-135 . DOI: 10.15672/HJMS.2019.667
MLA BALAN, V , PEYGHAN, E , SHARAHİ, E . "Statistical structures on the tangent bundle of a statistical manifold with Sasaki metric". Hacettepe Journal of Mathematics and Statistics 49 (2020 ): 120-135 <https://dergipark.org.tr/en/pub/hujms/issue/52287/535195>
Chicago BALAN, V , PEYGHAN, E , SHARAHİ, E . "Statistical structures on the tangent bundle of a statistical manifold with Sasaki metric". Hacettepe Journal of Mathematics and Statistics 49 (2020 ): 120-135
RIS TY - JOUR T1 - Statistical structures on the tangent bundle of a statistical manifold with Sasaki metric AU - Vladimir BALAN , E. PEYGHAN , Esa SHARAHİ Y1 - 2020 PY - 2020 N1 - doi: 10.15672/HJMS.2019.667 DO - 10.15672/HJMS.2019.667 T2 - Hacettepe Journal of Mathematics and Statistics JF - Journal JO - JOR SP - 120 EP - 135 VL - 49 IS - 1 SN - 2651-477X-2651-477X M3 - doi: 10.15672/HJMS.2019.667 UR - https://doi.org/10.15672/HJMS.2019.667 Y2 - 2018 ER -
EndNote %0 Hacettepe Journal of Mathematics and Statistics Statistical structures on the tangent bundle of a statistical manifold with Sasaki metric %A Vladimir BALAN , E. PEYGHAN , Esa SHARAHİ %T Statistical structures on the tangent bundle of a statistical manifold with Sasaki metric %D 2020 %J Hacettepe Journal of Mathematics and Statistics %P 2651-477X-2651-477X %V 49 %N 1 %R doi: 10.15672/HJMS.2019.667 %U 10.15672/HJMS.2019.667
ISNAD BALAN, Vladimir , PEYGHAN, E. , SHARAHİ, Esa . "Statistical structures on the tangent bundle of a statistical manifold with Sasaki metric". Hacettepe Journal of Mathematics and Statistics 49 / 1 (February 2020): 120-135 . https://doi.org/10.15672/HJMS.2019.667
AMA BALAN V , PEYGHAN E , SHARAHİ E . Statistical structures on the tangent bundle of a statistical manifold with Sasaki metric. Hacettepe Journal of Mathematics and Statistics. 2020; 49(1): 120-135.
Vancouver BALAN V , PEYGHAN E , SHARAHİ E . Statistical structures on the tangent bundle of a statistical manifold with Sasaki metric. Hacettepe Journal of Mathematics and Statistics. 2020; 49(1): 135-120.