According to a complaint filed by the woman, who wanted to pursue a PhD in accounts, she had earlier met the 50-year-old professor and expressed desire to enroll for the course in the college, a senior official at Kothrud police station here said.
"The professor told her there was only one seat available in the course and two applications. He promised to help her get admission in the PhD course," he said.
The professor called the woman to his cabin in the college on August 8 and allegedly sought sexual favours in return for help and later harassed her, he said.
"The woman, who recorded all the conversation with the professor, however, resisted his advances and left the cabin and narrated the incident to some of her local friends," the official said.
The woman yesterday approached the police station and filed a case against the professor under IPC section 354 (A) (punishment for sexual harassment), he said.
"We arrested the man late last night under relevant IPC sections. He will be produced in a court today," he said.