Saravana Kumar Perumal, who teaches at the National Institute of Fashion Technology or NIFT, has been arrested, according to a news report published on NDTV.com.
Kumar had allegedly posted obscene and threatening messages about the singer Chinmayi Sripada as well as her mother on both Twitter and Facebook, the report said.
Ms Sripada filed a police complaint on 18 October alleging that since January last year, "a few individuals have threatened to kill, rape and assault me on Twitter". She added that "there are aspersions cast on my character as well as a chronic steam of vulgar references and innuendoes even about my mother".
She listed six twitter handles and alleged that the same people "have also been saying I'm against Tamil...and that I have also taken up cudgels against Sri Lankan Tamils".
"This issue shows the plight of single mothers," Ms Sripada's mother told NDTV. "Women should be respected. I told Chinmayi to forgive them every time, but she was pushed".
According to police, the NIFT professor's mobile phone and broadband connection records match with the said tweets. The arrest has been made under the Information Technology Act 2005 and Prevention of Women Harassment Act.
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