One month went by since I came to National University of Singapore. Singapore is an island city-state located at the southern tip of the Malay Peninsula, which is almost as large as that of Tokyo 23 ward. It is an international modern city. Walking along the street, you will pass by many foreigners and hear conversation in various kinds of languages.
I am staying at the Department of Mathematics in NUS (National University of Singapore). The main campus of NUS is located in south west Singapore at Kent Ridge. Over 30,000 students from 100 countries study in this global University. There is a lot of traffic in the campus. We always use shuttle bus to move to another department or dormitory. There are a great many books in the central library. I was surprised to see a lot of Japanese books on history, social sciences, literature and so on.
I often discuss with Professor Leung, who is my host professor. We have a
Now I am studying the pinching problems for compact submanifolds in a
complex projective space. As Professor Leung's advice, I am reading some
papers about submanifolds in a sphere to get some ideas on computation. I
refer to Gauchman's results to prove some pinching theorems for compact
minimal submanifolds in a complex projective space with respect to the
second fundamental form in the maximal direction.
On the other hand, as another approach to study submanifolds in a complex space form, I am researching about g-Tanaka-Webster connection. Originally, Tanaka-Webster connection is defined as a canonical affine connection on a non-degenerate pseudo-Hermitian CR manifold. Recently, g-Tanaka-Webster connection for real hypersurfaces of Kaehlerian manifolds, which is an extension of Tanno's generalized Tanaka-Webster connection are studied. I got some results about the Ricci tensor and the shape operator of hypersurfaces in a complex space form with respect to this connection.
Department of Science
I study mathematics on weekdays, and walk around Singapore on holidays. The traffic system of Singapore is highly efficient. You can go everywhere in this country by bus and MRT, which is a rapid transit railway system. The most updated bus guide, "BUS GUIDE & BUS-STOP DIRECTORY" has 528 pages! And I can't go anywhere without using these transportation system, because the weather is hot and humid. Sometimes my glasses have fogged up when I got off the air-conditioned bus. Looking out of the window of MRT or a double-decker bus, I could get a good view of the city. There are a lot of modern tall buildings, especially in the central area. And many buildings and tourist facilities are under construction.
Around City Hall
My favorite place is the Singapore Botanic Garden, which is about eleven times as large as Tokyo dome. It was established in 1822 by Sir Stamford Raffles. The main attraction is the National Orchid Garden which has a collection of 60,000 orchids (more than 1,000 species 2,000 hybrids), the national flower of Singapore. We can also enjoy many sightseeing spots in the garden, like Ginger Garden, Swan Lake. It was so nice to walk around the garden, seeing deep green trees in the bright sunlight.
Finally, I'd like to express my gratitude to Prof. Leung for his help. And I am much obliged to this program for giving me such a great opportunity.