A fundamental result in the theory of minimal rational curves on projective manifolds is Cartan- Fubini extension theorem proved by Hwang and Mok, which describes the extensibility of biholomorphisms between connected...A fundamental result in the theory of minimal rational curves on projective manifolds is Cartan- Fubini extension theorem proved by Hwang and Mok, which describes the extensibility of biholomorphisms between connected open subsets of two Fano manifolds of Picard number 1 which preserve varieties of minimal rational tangents （VMRT）, under a mild geometric assumption on the second fundamental forms of VMRT＇s. Hong and Mok have developed Cartan-Fubini extension for non-equidimensional holomorphic immersions from a connected open subset of a Pano manifold of Picard number 1 into a uniruled projective manifold, under the assumptions that the map sends VMRT＇s onto linear sections of VMRT＇s and it satisfies a mild geometric condition formulated in terms of second fundamental forms on VMRT＇s. In the current paper, we give a generalization of Hong and Mok＇s result, under the same condition on second fundamental forms, assuming only that the holomorphic immersions send VMRT＇s to VMRT＇s. Our argument is different from Hong and Mok＇s and is based on the study of natural foliations on the total family of VMRT＇s. This gives a substantially simpler proof than Hong and Mok＇s argument.展开更多
Urban tourism space is the primary area where tourism activities occur and a key driver of regional tourism space evolution.To explore the correlation between population aggregation and urban tourism spatial heterogen...Urban tourism space is the primary area where tourism activities occur and a key driver of regional tourism space evolution.To explore the correlation between population aggregation and urban tourism spatial heterogeneity in the big data era,this study focuses on Wuhan’s main urban area in 2023.Using the Geographically Weighted Regression model,it analyzes the factors influencing tourism spatial heterogeneity.Additionally,Baidu Heat map data is employed to identify crowd aggregation levels during holidays,revealing the distribution patterns of urban tourism space.The results indicate that(1)factors derived from the GWR model significantly influence the number of tourism spaces in Wuhan,with evident spatial differences;(2)based on the spatial matching of heterogeneity factors and crowd aggregation levels,urban tourism space can be categorized into six types,including five core tourism spaces and other scattered spaces.This research highlights the spatial heterogeneity of urban tourism in Wuhan and provides a scientific basis for the transformation and quality improvement of urban tourism space by exploring the impact of population activity density.展开更多
基金supported by National Researcher Program of National Research Foundation of Korea(Grant No.2010-0020413)
文摘A fundamental result in the theory of minimal rational curves on projective manifolds is Cartan- Fubini extension theorem proved by Hwang and Mok, which describes the extensibility of biholomorphisms between connected open subsets of two Fano manifolds of Picard number 1 which preserve varieties of minimal rational tangents （VMRT）, under a mild geometric assumption on the second fundamental forms of VMRT＇s. Hong and Mok have developed Cartan-Fubini extension for non-equidimensional holomorphic immersions from a connected open subset of a Pano manifold of Picard number 1 into a uniruled projective manifold, under the assumptions that the map sends VMRT＇s onto linear sections of VMRT＇s and it satisfies a mild geometric condition formulated in terms of second fundamental forms on VMRT＇s. In the current paper, we give a generalization of Hong and Mok＇s result, under the same condition on second fundamental forms, assuming only that the holomorphic immersions send VMRT＇s to VMRT＇s. Our argument is different from Hong and Mok＇s and is based on the study of natural foliations on the total family of VMRT＇s. This gives a substantially simpler proof than Hong and Mok＇s argument.
基金supported by the Research Project on the Protection,Inheritance and Promotion of Yangtze River Culture in Hubei Province:Study on the Renewal Path of Urban Riverside Space in the Perceived Context of Yangtze River Culture Tourists(Project No.HCYK2024Y60)the Key Project of Philosophy and Social Science Research of Hubei Provincial Department of Education:Construction of Knowledge Atlas of Spatial Morphology of Traditional Villages in Hubei Segment of Yangtze River National Cultural Park(Project No.23D111)Innovation and Entrepreneurship Talents Program in Hubei Province(2023)(Project No.S202310488064).
文摘Urban tourism space is the primary area where tourism activities occur and a key driver of regional tourism space evolution.To explore the correlation between population aggregation and urban tourism spatial heterogeneity in the big data era,this study focuses on Wuhan’s main urban area in 2023.Using the Geographically Weighted Regression model,it analyzes the factors influencing tourism spatial heterogeneity.Additionally,Baidu Heat map data is employed to identify crowd aggregation levels during holidays,revealing the distribution patterns of urban tourism space.The results indicate that(1)factors derived from the GWR model significantly influence the number of tourism spaces in Wuhan,with evident spatial differences;(2)based on the spatial matching of heterogeneity factors and crowd aggregation levels,urban tourism space can be categorized into six types,including five core tourism spaces and other scattered spaces.This research highlights the spatial heterogeneity of urban tourism in Wuhan and provides a scientific basis for the transformation and quality improvement of urban tourism space by exploring the impact of population activity density.
