A study of curvature using infinitesimals

作者：Koike Satoshi^*; Kuo Tzee Char; Paunescu Laurentiu

来源：Proceedings of the Japan Academy Series A-Mathematical Sciences, 2012, 88(5): 70-74.

DOI：10.3792/pjaa.88.70

• Newton-Piuseux field
• curvature
• Lojasiewicz exponent
• gradient canyon
• Newton-Puiseux infinitesimals

Motivated by a profound observation of A%26apos;Campo we investigate the behaviour of the curvature of f(z, w) = c, f is an element of C{z, w}, vertical bar c vertical bar small, along infinitesimals. We use the language of infinitesimals as introduced in [2]. Along the way we introduce the important notion of gradient canyon, and prove several theorems in which this notion plays the key role. In this paper we give three such theorems and mention several other facts, to be published elsewhere.

• 出版日期2012-5